In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider [4], from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent risk measures. Consequently we discuss robus...

Traditional approaches to solving stochastic optimal control problems involve dynamic programming, and solving certain optimality equations. When recast as stochastic programming problems, structural aspects such as convexity are regained, and solution procedures based on decomposition and duality may be exploited. This paper explores a class of stationary, infinite-horizon stochastic optimizat...

The aim of this work is to construct the stochastic calculus of variations on Poisson space and some of its applications via the stochastic analysis on Wiener space. We define a new gradient operator on Wiener space, whose adjoint extends the Poisson stochastic integral. This yields a new decomposition of the Ornstein-Uhlenbeck operator and a substructure of the standard Dirichlet structure on ...

Decision making under uncertainty is a challenge faced by many decision makers. Stochastic programming is a major tool developed to deal with optimization with uncertainties that has found applications in, e.g. finance, such as asset-liability and bond-portfolio management. Computationally however, many models in stochastic programming remain unsolvable because of overwhelming dimensionality. F...

In this chapter we present a hybridization of a stochastic based search approach for multi-objective optimization with a deterministic domain decomposition of the solution space. Prior to the presentation of the algorithm we introduce a general formulation of the optimization problem that is suitable to describe both single and multi-objective problems. The stochastic approach, based on behavio...

We present a decomposition algorithm to solve a multi-level large scale quadratic programming problem with stochastic parameters in the objective functions. In the first phase of the solution algorithm and to avoid the complexity of this problem, the stochastic nature of the problem is converted into the equivalent crisp problem. In the second phase, Taylor series is combined with a decompositi...

We study the introduction of transitions with Phase-type distribution ring time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works...

This paper proposes a stochastic hydro unit commitment (SHUC) model for price-taker hydropower producer in liberalized market. The objective is to maximize the total revenue of producer, including immediate revenue, future (i.e., opportunity cost), and startup shutdown cost. market price uncertainty taken into account through scenario tree. solution challenging task due its non-convex high-dime...

We present a computational study of several strategies to solve two-stage stochastic linear programs by integrating the adaptive partition-based approach with level decomposition. A partition-based formulation is a relaxation of the original stochastic program, obtained by aggregating variables and constraints according to a scenario partition. Partition refinements are guided by the optimal se...

In this paper, we compare the availability and performance of a wireless TDMA system with and without automatic protection switching. Stochastic reward net models are constructed and solved by SPNP (Stochastic Petri Net Package). Hierarchical decomposition is adopted to simplify the analysis. The optimization of the number of guard channels reserved for the handoff calls is studied. Numerical r...