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Dear scientific community,
I would be very interested to hear your input regarding the scaling-up of LCA studies to a portfolio level. I know there is a plethora of product LCAs and plenty of them consider several individual products or product variants in parallel. However, I have not found an awful lot of studies that extend to several hundred, let alone thousands of individual products within the scope of one study (as opposed to equally as many individual case studies).
Surely, more people have approached this apparent research gap. So for anyone that has been active in this area: I would greatly appreciate you sharing what experience you have made or you pointing me at any related publications in the field.
Many thanks and best regards
Tobias
P.S: If you are interested what my colleagues and I have done in this field, feel free to check this framework article and the case study we presented at LCM 2021 conference:
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Tobias Manuel Prenzel Cradle-to-gate is an evaluation of a portion of a product's life cycle from resource extraction (cradle) through factory gate (ie, before it is transported to the consumer). Cradle-to-gate evaluations are occasionally used as the foundation for business-to-business environmental product declarations (EPDs).
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Hi Friends,
I would like to make an article in Quantum Finance.
You know that computer giants such as IBM and D-Wave System have opened quantum computers over the cloud to the use of researchers, currently.
I want to do Quantum portfolio optimization using Quantum computers using different financial assets (Stock, currency, gold, crypto).
I have tried with D-Wave System but I still haven't been successful:/ It is really diffucult.
Can you help me or give me an idea about this?
Thank you very much
Best Regards
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Interesting topic.
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I am working on portfolio optimization using lower partial moment of order 1, can someone help me how to implement LPM-1 in excel sheet using "tau" as my threshold value as 0.00% and order (n) as 1.
Thank you all in advance for your contributions to my question.
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For orientation I am looking for theories as a basis of an goal-based investment approach. So far I found some appraoches using
  • Portfolio Optimization with Mental Accounts (POMA)
  • Asset Liability Management (ALM)
  • Stochastic Dominance (SD)
Do you have any other suggestions?
Which approach is most common and accepted?
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Based on the substitution of personal goals for market goals - these are more theories from the field of behavioral finance. As we say: a tit in the hand is better than a crane in the sky!
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What is the best way to construct investment portfolios: based on asset prices or based on the changes in asset prices through time? E.g., if Asset A is 55 in 2010 and 60 in 2011, should I use 55 and 60 as data points or should I use 5 (i.e, 60 minus 55)? Thank you in advance.
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Jan H Jansen there is a chapter on "Fractionally Differentiated Features" in Lopez de Prado's "Advances in Financial Machine Learning". It deals with the trade-off between making time-series stationary by using returns and the memory-loss that is generated by doing so.
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Hi,
I want to calculate the correlation of the Bitcoin price with some other asset classes such as gold or oil. Therefore, I use the daily returns in percent of each asset and simply apply the correlation formula in excel. To be sure I got me two different datasources for oil and gold (Krugerrand and H&H gold, Texas and London Oil). Obviously the historic prices of Krugerrand and H&H are almost the same, the same applies for the two different kinds of oil.
My question/problem is: The correlation of the absolute values from Gold 1 - Gold 2 and Oil 1 - Oil 2 is close to one which makes sense. The correlation of the returns, however, is close to zero, i.e. non existent. How can that be? shouldn't the returns be at least very positively correlated as well?
Furthermore, the correlation of each time series with Bitcoin differs, even though I am thinking that Oil 1 and Oil 2 / Gold 1 / Gold 2 should have the same relation to Bitcoin.
I am trying to figure this out since days now and I am running out of time for this project. I would really appreciate if anyone has an idea what I am not seeing here.
I attached the excel, the most relevant sheets are highlighted in red.
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The calculation of the correlation is done based on the time invariant data pairs (xi,yi). For the calculation of the returns the derivative between 2-time steps is considered, right. This is in principle something different and here we see a nice example that this can lead to interesting results.
The correlation of the day by day return is zero. Conclusion: there is no intraday correlation between these two values.
But there might by a correlation between day i and day i+n. So try to correlate (xi,yi+1), (xi, yi+2),… and you will observe an interesting result 😉. Hope that helped – and good luck.
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  • Is there a benefit of having lower gap between 'in-sample' variance of portfolio daily returns and 'out-of-sample' variance of portfolio daily returns? (= better estimates the out-of-sample variance)
Question in more detail
  • I have developed a way of optimizing a portfolio, based on Global Minimum Variance portfolio optimization.
  • There are upside and downside of my portfolio optimization method.
cons : It cannot lower the `out-of-sample variance' of portfolio daily returns than the GMV portfolio. In other words, my portfolio optimization method fails to achieve better portfolio performance such as Sharpe ratio.
pros : However, my portfolio optimization method has lower gap between 'in-sample variance' and 'out-of-sample' variance than the GMV portfolio.
  • For illustration, let me give you an example. During training period to come up with how much weight to put on each stock, GMV portfolio optimization calculates the stock weight with variance 100 of daily returns. However, during the investment period (test period), it gives me 125 for 'out-of-sample' variance.
  • My portfolio method gives me 150 variance for 'in-sample variance' and 130 for 'out-of-sample' variance. As you can see, the actual variance is still low with the result of GMV portfolio optimization method. However, my method expects the 'out-of-sample' variance better than GMV method. GMV method is wrong by 25 percent, while my method is wrong by 13 percent.
  • As such, I am curious to know if my portfolio optimization method would be useful in any case of trading in stock market nowadays.
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I agree, you should test if the differences are statistical significant with a chi-squared test. I guess, probably they are not, according to my experience.
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How do you approach the selection and implementation of an information system for managing projects, programs and portfolios in an organization? What are the main criteria for choosing and implementing a management information system you can recommend?
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Krystsina Mazhei great question. The PMO often includes portfolio management responsibilities along with a team of project managers actually carrying out projects. It's more than establishing rules and guidelines for project management, the PMO should be delivering value.
Based on over 10 years of work with Fortune 500 companies, the biggest mistake PMO's make when selecting a portfolio management system (PPM) for their PMO is not accounting for their current state maturity. The failure rate of these tools is high, and while there are a few key reasons for failure, part of the problem is the lack of user adoption due to a complex tool.
According to research by Gartner, 80% of PMO's are only level 1 or level 2 maturity (out of a 1-5 scale on the capability maturity model). Unfortunately, most PMO's select software that is more sophisticated than what the PMO can actually use.
I have written more about these problems in an article here:
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Price optimization methods and algorithms are used to determine the best price or set of prices for business offerings by companies. In our project https://www.researchgate.net/project/Dynamic-Pricing-Algorithms-and-Models-using-Artificial-Intelligence
We are working on Dynamic Pricing Algorithms and Models using Artificial Intelligence. However we would like to hear from researchers experts about dynamic pricing models and algorithms. What are the best of breed Dynamic Pricing Algorithms and Models using Artificial Intelligence?
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I am an undergraduate student and in a project I am using copula to get multivariate distribution and use this distribution to get optimal weights of my portfolio in different risk measures(VaR/ CVaR/ Draw-downs). Although, there are enough research paper available but It would be really helpful if someone please suggest me some Programming in R for risk measures(VaR/ CVaR/ Draw-downs).
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The best reference you can have is McNeil, A. J., Frey, R., & Embrechts, P. (2005). Quantitative risk management: Concepts, techniques and tools (Vol. 3). Princeton: Princeton university press. In chapter 7. Programming in R that measures is not a soft problem but, you can look at my last paper in Risk Management journal, Cardona, E., Mora-Valencia, A. & Velásquez-Gaviria, D. Risk Manag (2018). https://doi.org/10.1057/s41283-018-0046-z.
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Most prefered:- Investment optimization as an extension of Unit Commitment for a Portfolio consisting energy generation Units.
- Unit commiment
- Investment Optimization
- Economic dispatch
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- Long Term investment decision.
- Maximize gains
- Main constraint is to fulfill the demand
- Capturing all the uncertainities.
- Deterministic.
- Energy economy dispatch.
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I'm a big fan of the IRR approach for ranking projects. But none of these cash flow methods takes into account the opportunity costs of negative externalities.
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Mixed-Integer Linear Programming,
Exact algorithm
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Try find and read recommendation about project portfolio planning from PMI Standard for Portfolio Management (overview is available at https://www.pmi.org/learning/library/pmi-standard-portfolio-management-8216).
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The project is to maximize the Net Present Value of Heat generating power plants in a District heating system.
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Here are some arguments for/against some of the methods:
1) For the PV approach and perpetuity, you would need a discounting rate. The assumption of a constant discounting rate is often not true. In the case of power plants, you would probably discount some benefit amount in dollars (which is a random variable) with some interest rate (a random variable as well).
2) The PV and perpetuity assume that the power plant will not burnt down (during n periods or in perpetuity), which is surely impossible. Any potential risk and uncertainty are usually assumed to be zero in both of the methods.
3) Often these projects are decided by politicians, who cannot think over their legislation periods. So perpetuity method is surely not ideal for these particular cases.
4) Annuity only shows information from one single period and hinders differentiation between high-risk and low-risk investments.
5) Assuming risk and interest rate volatility are not issues, perpetuity shows the net asset value the best. Ownership can be transfered at any time with the same price. PV would assume that the power plant will be priced with 0$ after n periods.
In short: Each approach has assumptions. You may prefer one to the other, if you are sceptical about the assumptions in your case. On the other hand, if you do not take any assumption, your calculation may only contain minimal information.
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- Using Mixed integer liner programming.
- I need to determine the optimal timing to invest(maximizing Net Present Value) in district heating power plants and at the same time minimizaing Carbon emissions.
- Main constraint: coverage of a given heat demand.
- Investment decision through mixed integer linear programming.
- Investment optimization as extension of unit commitment. (schedule optimization)
- Deterministic approach.
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Thanks a lot Mr. Temitayo Bankole !
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- Investment optimization as an extension of unit commitement Optimization(Schedule Optimization).
- District Heating
- Revenue streams are Heat and Electricity.
- Main Objectives:- Optimization of Investment and Carbon emission
- Main constraint: coverage of a given heat demand.
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How a model using Mixed Integer Linear Programming can be made for 'Real Option Analysis' for an Investment decision?
I hope now it makes sense.
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Using Mixed Integer Linear Programming
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Dear sir
I have many papers about dispersed power generation included microturbine, fuel cell, photocell,.... you can see it in my page in researchgate.
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1) Main constraint: coverage of a given heat demand.
2) Investment decision through mixed integer linear programming.
3) Investment optimization as extension of unit commitment (schedule optimization)
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IRR and NPV are best suitable methods
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I am working on a project in which I need to optimize the scheduling of heat generating power plants.
I want to Maximize Net Present Value and at the same time minimize Carbon emission.
Mixed integer liner programming will be used through out the modelling.
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I think you can use global algorithm that observe all of equations
Well, first you should find an equation or a function in order to find the value of two variables
then you can use GA algorithm or PSO algorithm
please check the following links
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Does anyone have research insights on whether Millennials and their investment needs and habits differ from those of their parents? And if so, how they differ?
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I'm looking for some advice for a suitable technique for optimising subject to constraints. My initial problem started out as a basic simplex optimisation problem finding a weight vector $w$, but now I'm trying to add more special constraints. I've heard of techniques to transform absolute function constraints into multiple linear constraints, but I don't know about sign functions. Here is my problem: given input values $x_{i}^{j}$ and $y_{i}^{j}$, I'm trying to find a weight vector $w_{i}^{j}$ to optimise:
\[ \sum^{m}_{j=1}\sum^{n}_{i=1}(w_{i}^{j}+1)y_{i}^{j} \]
subject to:
\[ \sum^{m}_{j=1}\left| \sum^{n}_{i=1}w_{i}^{j}x_{i}^{j}\right| \leq H \]
and
\[ -1 \leq w_{i}^{j} \leq 1 \] for all $i$ and $j$
and
\[ \left|\sum^{n}_{i=1}w_{i}^{j}x_{i}^{j}\right|\leq \left|\sum^{n}_{i=1}x_{i}^{j}\right| \] for all $j$ and
and
\[ sign\left(\sum^{n}_{i=1}w_{i}^{j}x_{i}^{j}\right) \left(sign\left(\sum^{n}_{i=1}w_{i}^{j}x_{i}^{j}\right) + sign\left(\sum^{n}_{i=1}x_{i}^{j}\right) \right) = 0\] for all $j$
Any advice anyone can give would be greatly appreciated, I dont really want to go down the Genetic Algorithm route straight away, if theres a numerical programming technique that is suitable I'd prefer to work with that and if this can be transformed into basic linear constraints and I can carry on using simplex optimisation that would be great!
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Thank you very very much guys, apologies for my vagueness I meant to say its maximise, its my first attempt using Latex since my PhD many years ago. Thank you for the suggestions, my only real experience of operational research was a 2nd year course during my maths undergrad where I learnt about the simplex method. I had a quick look at CPlex it does indeed have a lot more functionality than the standard Microsoft Solver Foundation I'm currently using. As you mentioned I am just using those sign functions like logical or statements, I didn't even realise you could use logical constraints like that, could be very powerful for my research and far more intuitive for my applications.
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I'm trying my hand at this problem.
I have two portfolios created with different strategies and different samples of the same investment universe. How can I determine if performance differences are statistically significant? I have several tests available to evaluate efficient frontier with ex-ante data (Spanning test; or Gibbons, Ross, and Shanken (1989) - those I prefer).
My problem is the evaluation of ex-post performance.
Can I still use Gibbons, Ross, and Shanken (1989)?
A simple test of difference in the means (t-statistics)?
Thanks to everyone who can help me, thanks for your time.
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Dear Alberto,
Please refer to one of my latest coauthored papers published in an A* ranked journal, European Journal of Operational Research (Attached Within):
Al Janabi, Mazin A. M., Arreola Hernandez, Jose, Berger, Theo, Khuong Nguyen, Duc, “Multivariate Dependence and Portfolio Optimization Algorithms under Illiquid Market Conditions”, European Journal of Operational Research, Vol. 259, No. 3, pp. 1121-1131, 2017. [Publisher: Elsevier, Inc.]
I hope it is useful!
Best Regards
Prof. Dr. Mazin A. M. Al Janabi
Full Professor of Finance & Banking and Financial Engineering
Tecnologico de Monterrey, EGADE Business School,
Santa Fe Campus, Mexico City, Mexico.
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I'm interested in financial economics and also I have ability to work with Artificial neural network and fuzzy logic.
is there any article about clustering or classification with financial approach?
Have you any idea about application of clustering and classification in financial markets?
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You might also find the following article written by Shaker A. Zahra useful:
Environment, corporate entrepreneurship, and financial performance: A taxonomic approach, Journal of Business Venturing
Volume 8, Issue 4, July 1993, Pages 319-340
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I want to optimize a portfolio based on regime switching model. Before optimization i need to detect the hidden regimes in the data. Let us suppose i want to start my analysis with GDP. What i want is to know the steps that are involved in identifying the regimes in a variable. There are many packages which do it. 
The first step is to download data for GDP. Then how should i proceed to detect the regimes. I will appreciate if some one just list the steps. For now i am not interested in the model or calculation. I just need to know what are the general steps in detecting the regimes in a variable.  
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Suppose that the GDP is observed at fixed intervals of time of length ∆. Let the total number of observation is N. Let S(i) be the observation at the end of i-th interval. Now calculate the return
  • r(i) =(S(i)−S(i−1))/S(i−1).
Choose n much smaller than N. A standard choice is n=20 whereas N is of the order 10^3 or more. For every i>n, calculate the moving mean ̄r(i) and moving standard deviation sd(i) of {r(i-1), r(i-2), ..., r(i-n)}
using
  • ̄r(i) =average of {r(i-1), r(i-2), ..., r(i-n)} and
  • sd(i)= √ (1/(n − 1) Σ0<j<n+1 (r(i-j)- ̄r(i))2).
The empirical drift μ(i) and volatility σ(i)  are given by
  • μ(i)=  ̄r(i)/∆
  • σ(i) = [sd(i)]/ √(∆).
Thus one obtains two different time series {μ(i)} and {σ(i)} respectively. The range of these are divided into finitely many disjoint parts, called regimes. After you decide your partitioning, for every i, look up where do μ(i) and σ(i)  belong. Furthermore, for every sub-interval, you may assign a representative value. 
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I want to optimize a portfolio in different horizon times.
can you help me what can I do and which software be suitable for this kind of problem? especially about portfolio re-balancing?
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I think LINGO
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For example, if we have returns of two assets A and B for six days, how can we calculate an equally weighted portfolio of these assets. 
   Time period               Return of Asset A                   Return of Asset B
    Day 1                            -0.710642873                           -5.393463923
    Day 2                            -0.710642873                           -5.393463923
            3                             -1.095970421                          -8.495258637
            4                             1.127622947                            2.971853106
            5                             1.417992995                           -2.789204653
            6                            0.419478214                           -2.027719244
please also share a relevant article of any good journal for reference.
Regards, 
Naveed
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Using equal or value weighted portfolios depend upon the problem... disagreement is there in application of Modern Portfolio Theory is to the performance of the use of above mentioned types. However in testing assest pricing models, normally equally weighted portfolios are constructed.....
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I'm currently doing my portfolio analysis with 30 stocks. I use FCM to cluster my data and use GA as my portfolio optimizer. I have 3 clusters. Every time I run my code in GA, my plot looks like the file attached below. It's ok to have an efficient frontier like that?
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If you want to you can take alook at my joint published paper on the Banking Sector Asset Management on my RG page, it shows how you can model and compute the results using fractal geometry for factorisation in four dimensions - 3 plotted, 1 visual which is relativistic and follows the sytem cybernetic resolution presrving the "Arrow of Time" postulate.
Earl Prof. Dr. SKM QC EPS Fellow (Indirect) MES MRES MAICTE
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Hey,
I'm currently looking for a scenario tree modeling the return of some stocks or indices. As scenario tree generation is not the focus of my work, but I need some to test my portfolio model, it would be nice, if someone could send me his work. There is no need that the data is up-to-date. Ideally the tree has 3-5 stages and 3-5 stocks/indices.
Thank you very much!
Jelto
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I am working on it and I am almost done with it just wait for few months. Other scenarios are there in literature which can guide you for asset  return. You can  use bound and bound algorithm and can try yourself.
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I'm currently working on PORTFOLIO Optimization for my research paper. I used GA to solve a multi-objective problem but instead of using binary number as a gene indicator/ chromosome I used real number. Then I normalized it for the weights to be equal to 1. Is it ok to use real numbers instead of binary numbers?
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Charlene Mae De vera Galang
If you use real number you will get more search space as compared to the binary one.
please go through the my publication for more detail or use the Goldberg's book.
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Hey,
I'm looking for a way to model different kinds of transaction costs (bid-ask spreads, brokerage commissions, market impact costs, transaction taxes) in a multi-period risk minimimzation model. 
In papers dealing with multi-period portfolio optimization you can often find proportional transaction cost, which doesn't seem to be very realistic. Do there exist good alternatives which lead to a "solvable" optimization problem? Are there any best practices from active traders available?
Thank you!
Jelto
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Linear (on trading volume) market impact model IS realistic with the given time of execution. Please take a look at my paper "Market Impact Paradoxes".
I implemented multi-period portfolio liquidation scheme for Deutsche Bank and later provided short description in another paper " Statistical  Arbitrage: medium Frequency Portfolio Trading". So, it is a real model that works.  
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Hey,
in the moment I'm dealing  with time consistency for optimization problems in the sense of Shapiro(2009). My problem in the moment is, that I think that a minimal expected return constraint for the final wealth normally leads to time inconsistent problems but I cannot find any papers about this topic. Carpentier et al. (2012) adresses this question in the Markovian setting, but I cannot find anything for the general one.
This leads to my final questions: Is there some literature adressing the question, how far minimal expected return constraints have effect on the "degree" of time inconsistency of the optimization problem? Are there similar formulations (for example for intertemporal return) that are mitigating this problem?
Thanks for your help.
Jelto
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Dear Jelto Borgmann
Greetings,
Please find the three attached files about the literature review about your question related for your topic may be useful for you and good luck
Best Regards,
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I am still struggling to understand the exact differences between Multi-attribute Decision Making (MADM) and Multi-objective Decision Making (MODM). From what I know a major difference is the solution space (discrete vs continuous).
Could someone provide me with a practical example to illustrate that difference? An (project) portfolio selection example would be even more helpful.
Thanks a lot!
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For simplicity, I will take only three attributes for portfolio selection. Let there be five IT companies c1,...,c5 and three attributes, namely profit, debt equity ratio and eps. We collect past data of three attributes for these five companies. You can also see this data as 5 points in three dimensional space. Out of these five points, we have to select the best one using some criterion. Thus, it became a problem of selection from a finite set. This is MADM.
Now consider the following problem. I have taken this problem just randomly to explain. It may not have any solution.
Max f1=x1+x2-x3;
Min f2=x1-2*x2+3*x3;
subject to
g1(x1,x2)=3*x1+4*x2-x3<=5;
-1<=x1<=1, 2<=x2<=3; -2<=x3<=4;
Between the specified range of x1,x2 and x3 and those points which satisfy g1 also, there are infinitely many points from which I want a point which maximizes f1 and minimizes f2 simultaneously. These points are also from three dimensional space but the number of points are infinite. We are not given limited alternatives. In this case we have infinite alternatives. This is MODM.
I hope now you might have understood the difference.
For your kind information, our paper on portfolio selection is in press. I will upload it when it is published.
Unfortunately, I was not so active in Q&A when you asked the question. So, too late answer.
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Hey everybody,
I'm dealing with time consistent portfolio optimization (as done in Yang,Cheng, Zhang 2015)  and I want to show, that the nested CVaR defined for a wealth process (X_t, ..., X_T) by
ComCVaR_{T,T}(X_T) = - X_T
ComCVaR_{t,T}(X_t,..., X_T} = CVaR(-ComCVaR_{t+1,T}(X_t+1,..., X_T}| F_t) - X_t
leads to inconsistent policies in the sense that the future planned decisions are not going to be implemented when running the optimization problem (Min ComCVaR) at a later time stage. Are there any easy examples in the form of scenario trees which show the time inconsistency of the optimal policy in the literature or can they be constructed easily? Have not found any up to now.
Thanks for your help!
Jelto
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Hey Jelto,
I remember seeing in a paper (unfortunately I do not remember exactly the author and title) an example which included a sample graph with distances between different points and the time required to travel the distances. Then some of the timings are allowed to change depending on the presence/lack of traffic jams (so depending on the point of time where you get information about traffic jam your original estimates of the best way may change).
I think a similar approach may be taken with a tree (instead of a graph) and estimated losses (instead of time) and special economic events (instead of traffic jams).
Best regards,
 Stan
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Graph algorithms like connectivity,search etc. I have read research work on MST algorithms and work of Mantega (Hierarchical structures in Financial Markets).
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If you want grand unified theory of portfolio optimisation using graphs you can read a number of my papers especially the ones on Asset Management on my RG webpage.
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Is there already some research going on, trying to generalize the work from Rockafellar and Uryasev (Optimization of  conditional value-at-risk) to non-coherent risk measures induced by OCEs? The only thing I found was a paper from Natarajan, Sim and Uichanco  (Fractable Robust Expected Utility and Risk Models), who are using piecewise linear utility functions. But it seems difficult to use this for larger problems, or am I wrong?
Looking forward for getting some interesting input!
Jelto
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I hope that my working paper "Applications of Risk-Sensitive Value Measure Method to Portfolio Evaluation Problems" shall help your research.
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If I have one year of daily closing prices of S&P 500 stocks (the first 100, alphabetically by ticker, with a full year of data from January 9, 1998 to January 8, 1999), then how can I scale it for a portfolio holding period of 20 days?
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The non-linearity of the equations coupled with the feedback process makes the resulting values tend to infinity; that is why we need a few attractors parameters to maintain the range within reasonable amounts.
What we are saying that we view thinking about the climate: all good hurricane hovers around a vortex, otherwise, the storm would disrupt and was extinguished quickly.
The simplest attractor of markets is its mean, that is, the values may disperse but tend to return to around the average. Hence, assuming that markets respond to a chaotic type model then we talk about the creation of fractals markets. This is the sensitivity to initial conditions (price ex post) is one of the attributes of chaos, the pattern is identical to that produced by a random IFS certain pairs of prices excluded
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when i run CVaR portfolio model in matlab i can just see final variable but i also need simplex final tableau.
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There are at least two ways to reach the goal. 1. Create portfolio optimization algorithm from stratch (in Matlab or any other language), so that you have access to all interior variables, including the final simplex tableau. 2. Use a third party portfolio optimization algorithm implemented (say) in Matlab. In the latter case answering your question requires having the third party code in front of ones eyes. Cuold you please point to the place where the code resides?
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I just have a Electre tri software.
I'm going to compare some sorting methods (around 5) in a stock portfolio problem. then I should find some proper sorting methods and softwares.
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Hi Seyed,
There are several software available. Find here some pointers. Best is to contact the authors if you are interested in their method.
- FlowSort  sorting method (based on Promethee methodology): www.smart-picker.com  --> there is a trial version and also research licences
- FINCLASS (Multicriteria Decision Support for Financial Classification Problems) (in Newsletter, Series 3, No. 3, Spring 2001): http://www.cs.put.poznan.pl/ewgmcda/pdf/SWFinclass.pdf
Other references:
Best wishes,
Philippe
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As both the mu vector and the S matrix suffer from estimation errors Robust portfolio optimization and robust portfolio estimators is a subject of interest. How can the Mahalanobis Distance be applied in portfolio optimization theory?
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Dear Anirban,
My approach to the problem you describe has been to integrate a Kalman Filter for estimating the joint returns distribution (under a linear Gauss-Markov dynamics assumption) into a multi-objective optimizer, which is an anticipatory metaheuristic.
One of the most important aspects when integrating predictive knowledge into an optimizer is to define a proper and better suited optimization model.
Thus, in my doctoral research, I've devised the so-called Anticipatory Stochastic Multi-Objective Optimization (AS-MOO) model, which is a multiperiod recurrence equation explicitly incorporating predictive knowledge about the future moments of factored returns distributions, for each Pareto-efficient candidate portfolio.
Perhaps you will find the following attached publications useful.
Best regards,
Carlos.
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Does out of sample performance of minimum variance portfolios improve when the estimates of the optimizer is a high dimension covariance matrix with high-frequency data and realized volatility approach? 
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Thanks Markus
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Using the historical var-cov matrix as an input in the optimizer leads to estimation errors. What other methods can be used in estimating the var-covar apart from shrinkage and diagonal methods?
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Implied Volatility as it is only the market's prediction of it from a Black- Scholes model, with quoted option prices , need not necessarily follow the statistical properties of a variance- co variance matrix .'Volatility smile' is an example for it
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I am considering which algorithm to use for Multi-class classification of credit risk scores.
I have a training set of ~100 default rates... and another transaction history of 1000 companies.
The idea is to classify in 5 groups A, B, C, D, E
My plan was to use Support Vector Machine for Mult-class. but I am open for new ideas.
Thanks
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There are two things that I would advise is:
a)As Sylantyev mentioned the time period is important due to crisis post-crisis period. you should test the data to see if the features correlate to the time periods. Also, see if shorter time periods have an effect on the data (spot cyclical or specific time periods which might bias the data)
b) At the stage that you are mentioning right now it is better to test several algorithms and not just one. Unless you have previous literature that already has done the work for you, I would suggest that you try several methods.