Atılım University Mathematics Department Seminars

Optimal Control Problems of Stochastic Differential Equations with New Runge-Kutta Methods
Hacer Öz
Atılım University, Turkey
Özet : In this work, we obtain the symplectic partitioned Runge-Kutta (SPRK) scheme for the optimal control problem of stochastic differential equations (SDEs). In order to discretize the optimal control problem, there are two basic approaches: discretize-then-optimize and optimize-then-discretize. We mainly focus on SPRK scheme for the optimal control problem of SDEs by following the discretize-then-optimize approach. After we present Hamiltonian formulations for the stochastic optimal control problem, we discretize the cost functional and the state equation with the help of Runge-Kutta schemes. To obtain the optimality system, we state the discrete Lagrangian. Then, we get the stochastic adjoint pair. (Our main contribution is to obtain an implicit Runge-Kutta scheme for the adjoint pair. As applications, we choose some problems from finance. We compare the numerical results with the exact solutions.
  Tarih : 09.03.2016
  Saat : 15:45
  Yer : FEF 404 - Seminar Room
  Dil : English