An efficient algorithm for stochastic optimal control problems by means of a least-squares Monte-Carlo method

Oz Bakan H., Yilmaz F. N., Weber G.

OPTIMIZATION, cilt.71, sa.11, ss.3133-3146, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 71 Sayı: 11
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/02331934.2021.2009824
  • Dergi Adı: OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.3133-3146
  • Anahtar Kelimeler: Stochastic optimal control, discrete optimality conditions, least-squares Monte-Carlo method, Runge-Kutta method, optimization, OPTIMIZATION, APPROXIMATION, SIMULATION
  • Gazi Üniversitesi Adresli: Evet

Özet

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 pn is obtained in terms of conditional expectations E[p(n+1)] and E[p(n+1)Delta 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 leastsquares Monte-Carlo method.