Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints: Sample-Path Analysis
S. Ilker Birbil
Sabanci University - Graduate School of Management; Erasmus Research Institute of Management (ERIM)
Tilburg University - Center for Economic Research (CentER)
affiliation not provided to SSRN
18 2004 2,
ERIM Report Series Reference No. ERS-2004-016-LIS
We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated. Such programs can be used for modeling \average" or steady-state behavior of complex stochastic systems. Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. The convergence analysis of sample-path methods rely heavily on stability conditions. We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence. Alongside we provide a complementary sensitivity result for the corresponding deterministic problems. In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.
Number of Pages in PDF File: 28
Keywords: stochastic mathematical programs with complementarity constraints, sample-path methods, simulation, stability, regularity conditions, mathematical programs with equilibrium constraints
JEL Classification: M, M11, R4, C62
Date posted: March 20, 2004
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