Now showing items 1-10 of 22
A class of stochastic programs with decision dependent uncertainty
The standard approach to formulating stochastic programs is based on the assumption that the stochastic process is independent of the optimization decision. We address a class of problems where the optimization decisions ...
Variance reduction in sample approximations of stochastic programs
This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sample approximations of stochastic programs. In high dimensional numerical integration, RQMC methods often substantially reduce the variance of ...
Two-stage integer programs with stochastic right-hand sides
A superadditive dual approach
We consider two-stage pure integer programs with discretely distributed stochastic right-hand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms ...
On the Fortet-Mourier metric for the stability of Stochastic Optimization Problems, an example
We consider the use of the Fortet-Mourier metric between two probability measures to bound the error term made by an approximated solution of a stochastic program. After a short analysis of usual stability arguments, we ...
Assessing policy quality in multi-stage stochastic programming
Solving a multi-stage stochastic program with a large number of scenarios and a moderate-to-large number of stages can be computationally challenging. We develop two Monte Carlo-based methods that exploit special structures ...
Arbitrage pricing of American contingent claims in incomplete markets - a convex optimization approach
Convex optimization provides a natural framework for pricing and hedging financial instruments in incomplete market models. Duality theory of convex optimization has been shown to yield elementary proofs of well-known ...
Conditional value-at-risk in stochastic programs with mixed-integer recourse
In classical two-stage stochastic programming the expected value of the total costs is minimized. Recently, mean-risk models -- studied in mathematical finance for several decades -- have attracted attention in stochastic ...
A stochastic programming approach to resource-constrained assignment problems
We address the resource-constrained generalizations of the assignment problem with uncertain resource capacities, where the resource capacities have an unknown distribution that can be sampled. We propose three stochastic ...