Iterative estimation maximization for stochastic linear programs with conditional value‐at‐risk constraints

Iterative estimation maximization for stochastic linear programs with conditional value‐at‐risk constraints

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Article ID: iaor20126356
Volume: 9
Issue: 4
Start Page Number: 441
End Page Number: 458
Publication Date: Nov 2012
Journal: Computational Management Science
Authors: ,
Keywords: iterative methods, portfolio optimization, stochastic linear programme, value at risk
Abstract:

We present a new algorithm, iterative estimation maximization (IEM), for stochastic linear programs with conditional value‐at‐risk constraints. IEM iteratively constructs a sequence of linear optimization problems, and solves them sequentially to find the optimal solution. The size of the problem that IEM solves in each iteration is unaffected by the size of random sample points, which makes it extremely efficient for real‐world, large‐scale problems. We prove the convergence of IEM, and give a lower bound on the number of sample points required to probabilistically bound the solution error. We also present computational performance on large problem instances and a financial portfolio optimization example using an S&P 500 data set.

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