Name
Abstract | ||
|---|---|---|
We introduce a stochastic dynamic optimization problem, where risk aversion is expressed by a stochastic ordering constraint. The constraint requires that a random reward sequence depending on our decisions dominates a given benchmark random sequence. The dominance is defined by discounting both processes with a family of discount sequences, and by applying a univariate order. We describe the generator of this order. We develop necessary and sufficient conditions of optimality for convex stochastic control problems with the new ordering constraint, and we derive an equivalent control problem featuring implied utility functions. Furthermore, we prove the existence of an optimal random discount sequence such that the solution of the risk averse problem is also a solution of an expected value problem with this discount. Finally, we derive a version of the maximum principle for the problem with discounted dominance constraints. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1137/070679569 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
optimal random discount sequence,discounted dominance constraint,convex stochastic control problem,discount sequence,stochastic dynamic optimization problem,random reward sequence,benchmark random sequence,expected value problem,stochastic dynamic optimization,discounted stochastic dominance constraints,risk averse problem,equivalent control problem,stochastic control,utility,stochastic programming,stochastic dominance,maximum principle,risk | Mathematical optimization,Stochastic optimization,Optimal control,Stochastic dominance,Semi-infinite programming,Stochastic programming,Optimization problem,Stochastic ordering,Mathematics,Stochastic control | Journal |
Volume | Issue | ISSN |
47 | 5 | 0363-0129 |
Citations | PageRank | References |
11 | 0.58 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Darinka Dentcheva | 1 | 345 | 25.80 |
| Andrzej Ruszczyński | 2 | 798 | 84.38 |