Études numériques et applications de processus d'approximation stochastique
Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation () based Sharpe ratio for measuring...
Expériences with Stochastic Algorithms fir a class of Constrained Global Optimisation Problems
The solution of a variety of classes of global optimisation problems is required in the implementation of a framework for sensitivity analysis in multicriteria decision analysis. These problems have linear constraints, some of which have a particular structure, and a variety of objective functions, which may be smooth or non-smooth. The context in which they arise implies a need for a single, robust solution method. The literature contains few experimental results relevant to such a need. We...
Experiences with stochastic algorithms for a class of constrained global optimisation problems
Gain-loss pricing under ambiguity of measure
Motivated by the observation that the gain-loss criterion, while offering economically meaningful prices of contingent claims, is sensitive to the reference measure governing the underlying stock price process (a situation referred to as ambiguity of measure), we propose a gain-loss pricing model robust to shifts in the reference measure. Using a dual representation property of polyhedral risk measures we obtain a one-step, gain-loss criterion based theorem of asset pricing under ambiguity of...
Genetic Algorithm Approach for Solving the Task Assignment Problem
This research was partially supported by the Serbian Ministry of Science and Ecology under project 144007. The authors are grateful to Ivana Ljubić for help in testing and to Vladimir Filipović for useful suggestions and comments.In this paper a genetic algorithm (GA) for the task assignment problem (TAP) is considered.An integer representation with standard genetic operators is used. Computational results are presented for instances from the literature, and compared to optimal solutions obtained...
Hybrid method for a class of stochastic bi-criteria optimization problems.
Hybrid search for optimum in a small implicitly defined region
Local stability and differentiability of the Mean–Conditional Value at Risk model defined on the mixed–integer loss functions
In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in~Schulz and Tiedemann [16]. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized...
Mapping the convergence of genetic algorithms.
Méthodes de simulation en programmation dynamique stochastique
Methods for solving stochastic bilinear fractional max-min problems
Modular production line optimization: The exPLOre architecture.
Multistage multivariate nested distance: An empirical analysis
Multistage stochastic optimization requires the definition and the generation of a discrete stochastic tree that represents the evolution of the uncertain parameters in time and space. The dimension of the tree is the result of a trade-off between the adaptability to the original probability distribution and the computational tractability. Moreover, the discrete approximation of a continuous random variable is not unique. The concept of the best discrete approximation has been widely explored and...
Multistage stochastic programs: The state-of-the-art and selected bibliography
Multistage stochastic programs via autoregressive sequences and individual probability constraints
The paper deals with a special case of multistage stochastic programming problems. In particular, the paper deals with multistage stochastic programs in which a random element follows an autoregressive sequence and constraint sets correspond to the individual probability constraints. The aim is to investigate a stability (considered with respect to a probability measures space) and empirical estimates. To achieve new results the Wasserstein metric determined by norm and results of multiobjective...
Necessary and sufficient optimality conditions for two-stage stochastic programming problems
Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming
We propose two methods to solve multistage stochastic programs when only a (large) finite set of scenarios is available. The usual scenario tree construction to represent non-anticipativity constraints is replaced by alternative discretization schemes coming from non-parametric estimation ideas. In the first method, a penalty term is added to the objective so as to enforce the closeness between decision variables and the Nadaraya–Watson estimation of their conditional expectation. A numerical application...
Notes on free lunch in the limit and pricing by conjugate duality theory
King and Korf [KingKorf01] introduced, in the framework of a discrete- time dynamic market model on a general probability space, a new concept of arbitrage called free lunch in the limit which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbitrage fails to have a basic property of other common concepts used in pricing theory – it depends...
Numerical study of discretizations of multistage stochastic programs
This paper presents a numerical study of a deterministic discretization procedure for multistage stochastic programs where the underlying stochastic process has a continuous probability distribution. The discretization procedure is based on quasi-Monte Carlo techniques originally developed for numerical multivariate integration. The solutions of the discretized problems are evaluated by statistical bounds obtained from random sample average approximations and out-of-sample simulations. In the numerical...