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An efficient algorithm for stochastic optimal control problems by means of a least-squares Monte-Carlo method.
- Source :
-
Optimization . Nov2022, Vol. 71 Issue 11, p3133-3146. 14p. - Publication Year :
- 2022
-
Abstract
- In this work, we provide discrete optimality conditions of the optimal control problems of stochastic differential equations. Euler and Runge–Kutta methods are used for discretization. A Lagrange multiplier method for a discrete-time stochastic optimal control problem is formulated. The discrete adjoint process p n is obtained in terms of conditional expectations E [ p n + 1 ] and E [ p n + 1 Δ W ] for both methods. To estimate these nested conditional expectations at each time step via simulation, we use a very powerful new approach, least-squares Monte-Carlo method, developed by Longstaff–Schwartz. This is the first time to solve a stochastic optimal control problem by calculating the nested conditional expectations numerically with the help of a least-squares Monte-Carlo method. Some examples are studied to test and demonstrate the efficiency of the Lagrange multiplier combined with the least-squares Monte-Carlo method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02331934
- Volume :
- 71
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 159812199
- Full Text :
- https://doi.org/10.1080/02331934.2021.2009824