Marida Bertocchi

University of Bergamo | UNIBG · Department of Management, Economics and Quantitative Methods

Multistage stochastic programs bring computational complexity which may increase exponentially with the size of the scenario tree in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal value are very useful. In this paper we provide monotonic lower...

We present two-stage stochastic risk averse optimization models for the power generation mix capacity expansion planning in the long run under uncertainty. Uncertainty is described by a set of possible scenarios in the second stage and uncertain parameters are the unit production costs of the existing power plants as well as those of the candidate...

Energy sector is facing a great level of importance in the globalized economy of industrial countries. Many actors are involved: producers, consumers, institutions, regulators and traders. Risk is present in each of the levels involving the various actors. This chapter explores the most common notions of risk used in this sector, describes the majo...

This chapter provides an overview of possible approaches that can be outlined to model and analyze the decision problems encountered in different stages of power production and delivery. The introduced models can be used for the control of two of the most important activities in power system management: production and transmission. In both cases, w...

The aim of this paper is to analyse the pricing of highly structured convertible bonds by taking a real world case. To this end we examine the Cashes (Convertible And Subordinated Hybrid Equity-linked Securities), which are characterised by both voluntary and mandatory conversion that depend on different triggering events, as well as floating coupo...

We introduce a model for analyzing the upgrade of the national transmission grid that explicitly accounts for responses given by the power producers in terms of generation unit expansion. The problem is modeled as a bilevel program with a mixed integer structure in both upper and lower level. The upper level is defined by the transmission company p...

We propose a multi-stage stochastic optimization model for the generation capacity expansion problem of a price-taker power producer. Uncertainties regarding the evolution of electricity prices and fuel costs play a major role in long term investment decisions, therefore the objective function represents a trade-off between expected profit and risk...

We present a single stage stochastic mixed integer linear model for determining the optimal mix of different technologies for electricity generation, ranging from coal, nuclear and combined cycle gas turbine to hydroelectric, wind and photovoltaic, taking into account the existing plants, the cost of investment in new plants, maintenance costs, pur...

In this study we analyze the chromatin state of human pluripotent stem cells by geometric and computational modelling of fibre conformation. The model takes into account local structure of chromatin organized into euchromatin, permissive for gene activation, and heterochromatin, transcriptionally silenced. Euchromatin was modelled using linear DNA...

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for optimal solution, may help in evaluating whether it is worth the additional computations for the stochastic program versus simplified approaches. In this paper we generalize measures from th...

Euro Bonds: Markets, Infrastructure and Trends presents the most recent developments in the Euro bond market. It discusses the problems of the Euro countries, the proposed solutions advocated by European as well as international institutions and investors. Particular emphasis is given to systemic risk and contagion as well as to specific innovative...

New kinematics of supercoiling of closed filaments as solutions of the elas-tic energy minimization are proposed. The analysis is based on the thin rod approxi-mation of the linear elastic theory, under conservation of the self-linking number. The elastic energy is evaluated by means of bending contribution and torsional influence. Time evolution f...

We propose a two-stage stochastic optimization model for maximizing the profit of a price-taker power producer who has to decide his own power generation capacity expansion plan in a long time horizon, taking into account the uncertainty of the following parameters: fuel costs; market electricity prices, as well as prices of green certificates and...

In this paper sensitivity analysis is adopted in order to reveal the role of randomness of a stochastic second-order cone program (Maggioni et al., 2009) for mobile ad-hoc networks starting from the semidefinite stochastic location-aided routing (SLAR) model, described in Ariyawansa and Zhu (2006) and Zhu et al. (2011). The algorithm looks for a de...

In this paper, we consider the problem of pricing life insurance contracts using ideas and methods taken from option pricing theory. The methodology developed is, rather general, however, to fix the ideas, we focus our attention on the problem of pricing a pure endowment policy that has its life contingent payout linked to the performance of a risk...

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for their optimal solution may help in evaluating whether it is worth the additional computations for the stochastic program versus simplified approaches. In this paper we present a summary of t...

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. In the two-stage case, several approaches based on different levels of available information has been adopted in literature such as the Expected Value Problem, EV , the Sum of Pairs Expected Values, SP EV , the...

We propose a stochastic model for the daily operation scheduling of a generation system including pumped storage hydro plants and wind power plants, where the uncertainty is represented by the hourly wind power production. In order to assess the value of the stochastic modeling, we discuss two case studies: in the former the scenario tree is built...

With the decline in the mortality level of populations, national social security systems and insurance companies of most developed countries are reconsidering their mortality tables taking into account the longevity risk. The Lee and Carter model is the first discrete-time stochastic model to consider the increased life expectancy trends in mortali...

We consider the optimal electric power generation capacity expansion problem, over a multi-year time horizon, of a price-taker power producer who has to choose among thermal power plants and power plants using renewable energy sources (RES), while taking into account regulatory constraints on CO2 emissions, incentives to generation from RES and ris...

A straightforward guide focused on life cycle investing-namely aging, retirement, and pensions Life cycle investing and the implications of aging, retirement, and pensions continues to grow in importance. With people living longer, the relative and absolute number of retirees is growing while the number of workers contributing to pension funds is d...

Introduction The Empirical Evidence Models for Portfolio Choices and Life-Cycle Asset Allocations Conclusions

Longevity and Changing Demographics Across the World The Evolution of Retirement Provision for Retirement

Equities ETFs: Exchange-Traded Funds Bonds and Fixed Income The Bond-Stock Measure for Medium-Term Large Crash Prediction Hedge Funds Real Assets Housing as an Asset Class Gold and Other Commodities Private Equity and Related Assets Currencies Evaluation of Great Investors Fundamental and Seasonal Anomalies of Asset Returns

Preserving Endowment Spending Devising a Rule So That Spending Never Falls References

Pillars of Retirement Reforming OECD Pensions Changing Role of Private Pensions Plans for Reforming Social Pensions Rethinking Pension Promises: Breaking the Fixed Link to a Monetary Value Intergenerational Risk-Sharing Conclusions Case Study: Public Sector vs. Private Pensions

Introduction Integrated Corporate/Pension Planning Model Assisting the Defined Benefit Pension System Conclusions

How Should Companies Fund Their Liabilities and Determine Allocations among Asset Classes and Hedging Instruments? Formulating InnoALM as a Multistage Stochastic Linear Programming Model Some Typical Applications Some Test Results Model Tests References

Introduction Types of Sovereign Funds Is There a Common Asset Allocation for Pension Funds? Sovereign Pension Funds and International Capital Markets Governance Issues of Public Pension Funds Regional Trends Conclusion References

Introduction Career Average Defined Benefit Schemes Cost Neutrality Choosing the Revaluation Rate The Adoption of Career Average Pension Schemes Advantages of a Switch to a Career Average Scheme Disadvantages of a Switch to a Career Average Scheme Redistribution Effects of a Switch to Career Conclusions

Own Company Stock The Role of Annuities The Role of Insurance The Role of Managed Withdrawal Plans Where and How to Retire? References

The Rudolf-Ziemba (2004) Intergenerational Surplus Management Model A Case Study Application of the Rudolf-Ziemba Model

A stochastic multistage portfolio model for a hydropower producer operating in a competitive electricity market is proposed. The producer’s portfolio includes the produced energy and a set of contracts for power delivery or purchase, including contracts of a financial nature such as forwards to be able to hedge against risks. The goal of using such...

A new stochastic model for mortality rate is proposed and analyzed on Italian mortality data. The model is based on a stochastic differential equation derived from a generalization of the Milevesky and Promislow model (Milevesky, M.A., Promislow, S.D.: Insur. Math. Econ. 29, 299–318 (2001)). We discuss and present a methodology, based on the discre...

New financial products and energy market strategies. Selected papers based on the presentations at the spring school of stochastic programming, Bergamo, Italy, April 10–20, 2007, and the 11th international symposium on stochastic programming (SPXI), Vienna, Austria, August 27–31, 2007

New financial products and energy market strategies. Selected papers based on the presentations at the spring school of stochastic programming, Bergamo, Italy, April 10–20, 2007, and the 11th international symposium on stochastic programming (SPXI), Vienna, Austria, August 27–31, 2007

In this paper sensitivity analysis is adopted in order to understand the randomness of a stochastic second order cone program for mobile ad hoc networks [3]. The algorithm looks for a destination node and sets up a route by means of the expected zone, the region where the sender node expects to find the destination node and the requested zone defin...

A stochastic multi-stage portfolio model for a hydropower producer operating in a competitive electricity market is proposed. The portfolio includes its own production and a set of forward contracts for future delivery or purchase of electricity to hedge against risks. The goal of using such a model is to maximise the profit of the producer and red...

The paper deals with a new stochastic optimization model, named Optimization Modelling for Gas Seller–Second Stochastic Version (OMoGaS–2SV), to assist companies dealing with gas retail commercialization. We consider temperature as a source of stochasticity, but we take into account also information on energy-related indices. Temperature influences...

We propose a two-stage stochastic second-order cone programming formulation of the semidefinite stochastic location-aided routing (SLAR) model, described in Ariyawansa and Zhu (Q. J. Oper. Res. 4(3), 239–253, 2006). The aim is to provide a sender node S with an algorithm for optimally determining a region that is expected to contain a destination n...

A fixed topology of stages and/or a fixed branching scheme are common assumptions for applications and numerical solution of scenario based multistage stochastic programs. Using contamination technique to test this structure, we extend the results of Dupačová (Contamination for multistage stochastic programs. In: Hušková M, Janžura M (eds) Prague s...

In this paper we value the impact of different distributional assumptions relative to Lee-Carter innovations in forecasting age-specific mortality in Italy. We fit the matrix with Italy death rates from 1960 to 2004, and we observe that the innovation series presents significant kurtosis. We implement the model approximating the innovations with a...

Stochastic programming is a tool to support bond portfolio management decisions. For a successful application of the stochastic programming methodology, one must choose an adequate model, asses its parameters, generate sensible input scenarios or scenario tree, solve the scenario-based problem using an optimization software and validate the results...

Abstract In this paper we study copula-based models for aggregation of operational risk capital across business lines in a,bank. A commonly,used method,of summation of the value-at-risk (VaR) measures, that relies on a hypothesis of full correlation of losses, becomes inappropriate in the presence of dependence,between business lines and may lead t...

The paper deals with a new stochastic optimization model, named OMoGaS–SV (Optimization Modelling for Gas Seller–Stochastic Version), to assist companies dealing with gas retail commercialization. Stochasticity is due to the dependence of consumptions on temperature uncertainty. Due to nonlinearities present in the objective function, the model can...

The integration of quantitative asset allocation models and the judgment of portfolio managers and analysts (i.e. qualitative view) dates back to a series of papers by Black and Litterman in the early 1990s. In this paper we improve the classical Black-Litterman model by applying more realistic models for asset returns (the normal, the t-student, a...

We examine the statistical properties of operational losses obtained from a large European bank using an actuarial-type framework. The simplistic assumption of a Poisson frequency distribution fails and we show that the frequency process follows closely a non-homogeneous Poisson process with a deterministic intensity of the form of a continuous cdf...

In this paper, the authors develop a stochastic optimization model, named Optimization Modelling for Gas Seller (OMoGas), to assist companies dealing with gas retail commercialization. Stochasticity is due to the dependence of consumption on temperature uncertainty. Nonlinearities are present in both the objective function and the constraints. The...

The price of defaultable or credit-risky bonds differs from the equivalent maturity price of a risk-free bond for a well identified number of factors: the positive probability of default prior to the bond maturity, the estimated loss given default, that depends on the adopted assumption on the recovery rate for that class, see Duffie and Singleton...

In this paper the authors propose an optimisation model, called OMoGaS (Optimisation Modelling for Gas Seller), to assist companies dealing with gas retail commercialisation. The model takes into account the limits on price imposed by law on small consumers as well as the gas company policies in order to explore the commercial consequences of diffe...

The paper deals with a new stochastic optimization model, named OMoGaS-SV (Optimisation Modelling for Gas Seller-Stochastic Version), to assist companies dealing with gas retail commercialization. Stochasticity is due to the dependence of consumptions on temperature uncertainty. Due to nonlinearities present in the objective function, the model can...

In this paper we develop two decision support procedures for the short-term hydro-thermal resource scheduling problem of a power producer operating in a liberalized market. These procedures, based on mixed integer LP models, determine the unit commitment of thermal units and the production levels of committed thermal units and available hydro plant...

To solve a decision problem under uncertainty via stochastic programming means to choose or to build a suitable stochastic programming model taking into account the nature of the real-life problem, character of input data, availability of software and computer technology. In applications of multistage stochastic programs additional rather complicat...

In this paper we develop a multi-factor model for the yields of corporate bonds. The model allows the analysis of factors which influence the changes in the term structure of corporate bonds. More than 98% of the variability in the corporate bond market is captured by the model, which is then used to develop credit risk immunization strategies for...

The paper deals with Eurobonds, which are a special category of corporate bonds characterized by a great variety of issuers and good liquidity. We suggest a model for pricing Eurobonds, based on Jarrow, Lando and Turnbull (1997) model for the bankruptcy combined with Black, Derman and Toy (1990) model of term structure of interest rates. The model...

The paper presents a state dependent multinomial model of intertemporal changes in the term structure of interest rates. The model is a one-factor interest-rate model within the Markov family models for short-term interest rate and it extends the Ho and Lee [J. Finance XLI (5) (1986) 1001] binomial model. We derive the theoretical basis of the mult...

The goal of this paper is to analyse by statistical methods the positions of individual countries within the EURO bond market. To this purpose we assume that each of the individual yield curves equals the sum of a common effect curve and of a country-specific one, interpreted as a spread. This allows to analyse the position of the countries by a tw...

The bond portfolio management problem is formulated as a multiperiod stochastic program using interest rate scenarios. The scenarios are sampled from the binomial lattice from a Black–Derman–Toy model. The paper analyzes the sensitivity of the solution of the resulting large-scale mathematical program with respect to the model inputs. The numerical...

Portfolio manager's performance is often evaluated respect to a predetermined market benchmark. Usually the benchmark is an equity/bond portfolio or index for which the percentage and the bond duration are specified, so the manager's aim is to build a portfolio whose performance replicates the benchmark performance. To achieve returns equal or high...

The bond portfolio management problem is formulated as a stochastic program based on interest rate scenarios. The coefficients of the resulting program are subject to errors of various kind. In this paper, we complement the theoretical stability results of by simulation experiments. Adapting the approach of to problems based on perturbed yield curv...

In this paper we present a model for management of bond portfolio including financing and investment repo contracts. Different specifications are suggested in order to reduce the problem to a linear programming problem and to consider a self-financing portfolio. The models are tested on historical data assuming a technical time scale equal to the m...

Management of bond portfolio is formulated as a multiperiod scenario-based stochastic program with random recourse. The former results on sensitivity analysis of its optimal value with respect to the strategy applied in selection of input scenarios are extended and applied to a real life problem from the Italian bond market. The numerical study pro...

Investments recommendations that result from scenario-based bond portfolio management models depend on the input scenarios which can be obtained in many different ways. Various aspects which influence the choice of representative scenarios for bond portfolio management, e.g., the sources of uncertainties and the level of the available information,...

Within the framework of sensitivity of the optimal value of the portfolio management problem described in Dupaeová and Bertocchi (1996), Dupaeová and Bertocchi (1997) with respect to lattice calibration, we compare Bjerksund and Stensland approximation algorithm, Kang Pan-Zenios algorithm and a modified Kang Pan-Zenios algorithm to generate short-r...

Some properties of M-matrices are investigated in order to analyze the closure of the class with respect to perturbations introduced in the matrix. An algorithm is derived by means of the implicit Gauss-Cholesky algorithm in the ABS class for linear systems: a lower estimation of the solution of linear system , where A is an M-matrix, and the solut...

The bond portfolio management problem is formulated as a stochastic program based on interest rate scenarios. It has been proved in Dupaková (1998) that small errors in constructing scenarios will not destroy the optimal solution. The aim of the contribution is to quantify, through carefully planned simulation studies, the magnitude of the above-me...

The contamination technique is presented as a numerically tractable technique for post-optimality analysis and analysis of the robustness of the optimal value of various scenario based stochastic programs with respect to inclusion of additional ‘out-of-sample’ scenarios. Using results based on the initial selection of scenarios and those based on t...

The contamination technique is applied to postoptimality anal ysis and analysis of the robustness of the optimal value of a scenario based bond portfolio management model with respect to inclusion of additional “out-of-sample” scenarios. Using results based on the initial selection of sce narios and those based on the alternative out-of-sample scen...

Management of bond portfolio is formulated as a multiperiod scenario based stochastic program with random recourse. Sensitivity analysis of its optimal value with respect to the strategy applied in selection of input scenarios is detailed and applied on a real life problem from Italian bond market.

Results of extensive computational experiments aimed at comparing performance quality (accuracy of an approximate solution and the running time) of the Threshold Accept (TA) approach versus the Simulated Annealing (SA) and a Greedy-Local improvement Search (GLS) approaches are presented. This comparison is done on a large set of test examples that...

Parallel computing has received increased attention from the scientific and business communities over the last five years or so. Reasons for the interest in this technological development are numerous. Just to name a few: limitations of the serial, von Neumann computer, economies of scale in manufacturing multiprocessors, the natural parallelism in...

A two-phase global random search procedure for solving some computationally intractable discrete optimization problems is proposed. Guarantees for quality of random search results are derived from analysis of non-asymptotic order statistics and distribution-free intervals that are obtainable in this way: the confidence interval for a quantile of gi...

A characterization of M-matrices is given by means of a special algorithm in the ABS class for linear systems. The effects of changes in the entries of the coefficient matrix are investigated. An application to the classical static Leontief and Sraffa input- output economic model is presented together with numerical results on a real case using an...

The paper aims to illustrate how parallel processing techniques may be used in solving option evaluation when the assumptions for using the Black and Scholes analytical formula are not satisfied. In such cases it is necessary to use numerical methods which are computationally quite expensive.

Approaches to parallel and symbolic computation in finance are discussed. They include applications for evaluation of primitive and derivative financial activities as well as interactions with expert systems tools. Financial mathematics often deals with modelling actual problems that require manipulation of huge amounts of data within hard time bou...

A computational study is performed of five conjugate gradient algorithms, including new methods based on the idea of nonlinear scaling, with various resetting strategies and different line search precision. The results show that algorithms of the Fletcher-Reeves type are significantly inferior to algorithms of the Polak-Ribière type, among which be...