Optimal Stopping with a Probabilistic Constraint
| Autor: | Alexander Vladimirsky, Aaron Zeff Palmer |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Stochastic control
050210 logistics & transportation Mathematical optimization Control and Optimization Applied Mathematics 05 social sciences Probabilistic logic Management Science and Operations Research 01 natural sciences Upper and lower bounds Dynamic programming Constraint (information theory) 010104 statistics & probability symbols.namesake Lagrangian relaxation 0502 economics and business Theory of computation symbols Optimal stopping 0101 mathematics Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications. 175:795-817 |
| ISSN: | 1573-2878 0022-3239 |
| Popis: | We present an efficient method for solving optimal stopping problems with a probabilistic constraint. The goal is to optimize the expected cumulative cost, but constrained by an upper bound on the probability that the cost exceeds a specified threshold. This probabilistic constraint causes optimal policies to be time-dependent and randomized, however, we show that an optimal policy can always be selected with “piecewise-monotonic” time-dependence and “nearly-deterministic” randomization. We prove these properties using the Bellman optimality equations for a Lagrangian relaxation of the original problem. We present an algorithm that exploits these properties for computational efficiency. Its performance and the structure of optimal policies are illustrated on two numerical examples. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink