Name
Abstract | ||
|---|---|---|
We consider stochastic optimization problems where risk-aversion is expressed by a stochastic ordering constraint. The constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector. We identify a suitable multivariate stochastic order and describe its generator in terms of von Neumann–Morgenstern utility functions. We develop necessary and sufficient conditions of optimality and duality relations for optimization problems with this constraint. Assuming convexity we show that the Lagrange multipliers corresponding to dominance constraints are elements of the generator of this order, thus refining and generalizing earlier results for optimization under univariate stochastic dominance constraints. Furthermore, we obtain necessary conditions of optimality for non-convex problems under additional smoothness assumptions. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s10107-007-0165-x | SIAM Journal on Optimization |
Keywords | DocType | Volume |
multivariate stochastic dominance constraint,optimality · duality · utility · stochastic order · risk,random vector,benchmark random vector,necessary condition,univariate stochastic dominance constraint,optimization problem,suitable multivariate stochastic order,morgenstern utility function,dominance constraint,additional smoothness assumption,stochastic optimization problem,stochastic optimization,stochastic dominance,stochastic order,lagrange multiplier,risk aversion | Journal | 25 |
Issue | ISSN | Citations |
1 | 1436-4646 | 23 |
PageRank | References | Authors |
0.92 | 5 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Darinka Dentcheva | 1 | 345 | 25.80 |
| Andrzej Ruszczyński | 2 | 798 | 84.38 |