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“School of Mathematics”

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Paper   IPM / M / 15364
School of Mathematics
  Title:   Approximating the solution of stochastic optimal control problems and the Merton's portfolio selection model
  Author(s):  Behzad Kafash
  Status:   Published
  Journal: Computational Economics
  Year:  2018
  Pages:   DOI: 10.1007/s10614-018-9852-3
  Supported by:  IPM
In this paper, a numerical algorithm is presented to solve stochastic optimal con3 trol problems via the Markov chain approximation method. This process is based 4 on state and time spaces discretization followed by a backward iteration technique. 5 First, the original controlled process by an appropriate controlled Markov chain is 6 approximated. Then, the cost functional is appropriate for the approximated Markov 7 chain. Also, the finite difference approximations are used to the construction of locally 8 consistent approximated Markov chain. Furthermore, the coefficients of the resulting 9 discrete equation can be considered as the desired transition probabilities and inter10 polation interval. Finally, the performance of the presented algorithm on a test case 11 with a well-known explicit solution, namely the Merton’s portfolio selection model, 12 is demonstrated.

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