Janos Mayer

• University of Zurich

Replicating Portfolios for Economic Capital Calculations

We show that the optimal asset allocation for an investor depends crucially on the decision theory with which the investor is modeled. For the same market data and the same client data different theories lead to different portfolios. The market data we consider is standard asset allocation data. The client data is determined by a standard risk prof...

We propose a numerical optimization approach that can be used to solve portfolio selection problems including several assets and involving objective functions from cumulative prospect theory (CPT). Implementing the suggested algorithm, we compare asset allocations that are derived for CPT based on two different methods: maximizing CPT along the mea...

Replicating portfolios have recently emerged as an important tool in the life insurance industry, used for the valuation of companies' liabilities. This paper presents a replicating portfolio (RP) model for approximating life insurance liabilities as closely as possible. We minimize the L1 error between the discounted life insurance liability cash...

In this chapter a general mathematical programming model of the scheduling problem as formulated in Sect. 1.2 is presented for the case where the electric power generation system includes thermal plants only. The model is called general because no simplifying assumptions are applied for the sake of obtaining a mathematical programming model tractab...

Both the generation system and the network transmitting electric power vary on a day-to-day basis; therefore, the daily optimization problems to be solved and their sizes also vary, although their structure remains essentially the same. This chapter shows how the daily scheduling problem, corresponding to the simplified model of the scheduling prob...

On the basis of the discussion in Chap. 3, the general model of the scheduling problem can be simplified. The simplified model is a large-scale mixed-variable mathematical programming problem with a linear objective function and linear constraints, with the coefficient matrix having a special structure. It is suitable for numerical solutions.

An electric power system is a combination of power-producing units, transmission lines, international cooperation, transformers, and a distribution network supplying customers with power under joint supervision and control.

In Chap. 2, our aim in formulating the general model of the scheduling problem was to construct a model that would best describe the problem, regardless of whether we had any chance of solving the corresponding mathematical programming problem. According to the overview of the model in Sect. 2.4, the corresponding problem is a large-scale, mixed-va...

We show that the optimal asset allocation for an investor depends crucially on the theory with which the investor is modeled. For the same market data and the same client data different theories lead to different portfolios. The market data we consider is standard asset allocation data. The client data is determined by a standard risk profiling que...

We compare asset allocations that are derived for cumulative prospect theory (CPT) based on two different methods: maximizing CPT along the mean {variance efficient frontier and maximizing CPT without this restriction. We find that with normally distributed returns, the difference between these two approaches is negligible. However, if standard ass...

We compare asset allocations derived for cumulative prospect theory(CPT) based on two different methods: Maximizing CPT along the mean–variance efficient frontier and maximizing it without that restriction. We find that with normally distributed returns the difference is negligible. However, using standard asset allocation data of pension funds the...

Coherent risk measures play an important role in building and solving optimization models for decision problems under uncertainty. We consider an extension to multiple time periods, where a risk-adjusted value for a stochastic process is recursively defined over the time steps, which ensures time consistency. A prominent example of a single-period...

For various SLP models with recourse, we present in this chapter properties which are relevant for the particular solution methods developed for various model types, to be discussed later on.

Linear programs have been studied in many aspects during the last 60 years. They have shown to be appropriate models for a wide variety of practical problems and, at the same time, they became numerically tractable even for very large scale instances.

The discussion of algorithms in this chapter is organized according to the framework of different SLP model classes, as presented in the previous chapters. A computer implementation of an algorithm will be called a solver.

In this article, decomposition methods for two-stage linear recourse problems with a finite discrete distribution are discussed. First, we cover the L-shaped decomposition method which represents a breakthrough concerning numerically efficient methods for solving two-stage recourse problems. This algorithm was the basis for the development of sever...

In this chapter we consider stochastic programming problems which represent a single decision stage. The decision is to be made “here and now” and the models do not account for any corrective (recourse) actions which might be available after the realization of the random variables in the model becomes known.

This paper presents a general reward-risk portfolio selection model and derives sufficient conditions for two-fund separation. In particular we show that many reward-risk models presented in the literature satisfy these conditions.

This paper presents a general reward-risk portfolio selection model and derives sufficient conditions for two-fund separation. In particular we show that many reward-risk models presented in the literature satisfy these conditions.

In this paper we suggest a behavioral foundation for the reward-risk approach to portfolio selection based on prospect theory. We identify sufficient conditions for two-fund separation in reward-risk models in general, and for the behavioral reward-risk model in particular. It is shown that a prospect theory investor with piecewise-power function s...

We develop an algorithm to compute asset allocations for Kahneman and Tversky’s (Econometrica, 47(2), 263–291, 1979) prospect theory. An application to benchmark data as in Fama and French (Journal of Financial Economics, 47(2), 427–465, 1992) shows that the equity premium puzzle is resolved for parameter values similar to those found in the labora...

Without Abstract

We consider classes of stochastic linear programming problems which can be efficiently solved by deterministic algorithms. For two–stage recourse problems we identify two such classes. The first one consists of problems where the number of stochastically independent random variables is relatively low; the second class is the class of simple recours...

We consider optimization problems for minimizing conditional value-at-risk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulate these CVaR optimization problems as two-stage recourse problems of stochastic programming. Specializing the L-shaped method leads...

We introduce the stochastic linear programming (SLP) model classes, which will be considered in this paper, on the basis of a small-scale linear programming problem. The solutions for the various problem formulations are discussed in a comparative fashion. We point out the need for model and solution analysis. Subsequently, we outline the basic ide...

This chapter describes the capabilities and the usage of SLP-IOR, our interactive model management system for stochastic linear programming (SLP). The main features of SLP-IOR are the following: the system is intended to support the entire life cycle of a model, including model formulation, analysis of the model instance, solving it, and analyzing...

We consider economies with additively separable utility functions and give conditions for the two-agents case under which the existence of sunspot equilibria is equivalent to the occurrence of the transfer paradox. This equivalence enables us to show that sunspots cannot matter if the initial economy has a unique spot market equilibrium and there a...

We consider economies with additively separable utility functions and give conditions for the two-agents case under which the existence of sunspot equilibria is equivalent to the occurrence of the transfer paradox. This equivalence enables us to show that sunspots cannot matter if the initial economy has a unique spot market equilibrium and there a...

The purpose of this paper is to discuss modeling aspects concerning multistage stochastic linear recourse problems. We will especially point out the additional features which arise when extending modeling support from two-stage recourse problems to the multistage case. The reason is that we have just finished the development of the first multistage...

Stochastic linear programming (SLP) models involve multivariate integrals. Although in the discretely distributed case these integrals become sums they typically contain a large amount of terms. The purpose of this paper is twofold:On the one hand we discuss the usage of bounds concerning integrals for constructing SLP algorithms and secondly we po...

This paper considers jointly chance constrained problems from the numerical point of view. The main numerical difficulties as well as techniques for overcoming these difficulties are discussed. The efficiency of the approach is illustrated by presenting computational results for large-scale jointly chance constrained test problems.

This paper gives a summary of selected testing features of the model management system SLP-IOR. The pseudo random test prob- lem generator GENSLP is described and numerical examples with randomly generated test problems are presented.

Solving a stochastic linear programming (SLP) problem involves selecting an SLP solver, transmitting the model data to the solver and retrieving and interpreting the results. After shortly introducing the SLP model classes in the first part of the paper we give a general dis-cussion of these various facets of solving SLP problems. The second part c...

In this paper stochastic linear programming (SLP) is considered from the model management point of view. General model management issues specific to SLP are discussed in connection with their implementation in SLP-IOR. The central topic of the paper is SLP-IOR itself which is a model management system for SLP be- ing under development by the author...

The purpose of the paper is to discuss the modeling process in stochastic linear programming (SLP) and to point out the SLP-specific features of computer support to this process.

A new mathematical programming model is presented for the computer color formulation problem. The model is essentially based on the two-constant Kubelka-Munk theory, that describes most of the necessary physical properties of this problem. The model is a nonconvex programming problem. It has a nonconvex objective function with some nice pseudoconve...

A duality relationship for the capacity of discrete memoryless channels is studied by means of geometric programming duality theory. A compulationally attractive dual approach and a family of algorithms which includes the classic Arimoto-Blahut method is proposed for the computation of capacity,

The subject of this paper is to give a survey on algorithms designed for the solution of probabilistic constrained problems with joint probabilistic constraints. A brief summary of the most important convexity results is also included as convexity properties play a central role in developing solution methods for this problem class. For overviews on...

The main purpose of this paper is to present a new mathematical programming formulation of the multiphase equilibrium problem along with a Newton-type algorithm for its solution. The approach pursued relies on the Gibbs free energy function and geometric programming duality. The problem arised in connection with a real-life problem in oil reservoir...

Some mathematical programming models of the mixing problem are discussed in this paper. Five models, based on different discrepancies, are considered and their fundamental properties are examined. Using variational and Smirnov distances, linear programming models are obtained. Pearson divergence leads to quadratic programming, Hellinger divergence...

The purpose of this paper is to investigate the possiblility to ap- proximate computationally multistage stochastic linear programs with arbitrary underlying probability distributions by those with finite dis- crete probability distributions—to begin with, just for the special case of only the right-hand-side being random.