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Approximating the Solution of Stochastic Optimal Control Problems and the Merton’s Portfolio Selection Model

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  • Behzad Kafash

    (Ardakan University
    Institute for Research in Fundamental Science (IPM))

Abstract

In this paper, a numerical algorithm is presented to solve stochastic optimal control problems via the Markov chain approximation method. This process is based on state and time spaces discretization followed by a backward iteration technique. First, the original controlled process by an appropriate controlled Markov chain is approximated. Then, the cost functional is appropriate for the approximated Markov chain. Also, the finite difference approximations are used to the construction of locally consistent approximated Markov chain. Furthermore, the coefficients of the resulting discrete equation can be considered as the desired transition probabilities and interpolation interval. Finally, the performance of the presented algorithm on a test case with a well-known explicit solution, namely the Merton’s portfolio selection model, is demonstrated.

Suggested Citation

  • Behzad Kafash, 2019. "Approximating the Solution of Stochastic Optimal Control Problems and the Merton’s Portfolio Selection Model," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 763-782, August.
    • Handle: RePEc:kap:compec:v:54:y:2019:i:2:d:10.1007_s10614-018-9852-3
    DOI: 10.1007/s10614-018-9852-3
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    References listed on IDEAS

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    1. Ieda, Masashi, 2015. "An implicit method for the finite time horizon Hamilton–Jacobi–Bellman quasi-variational inequalities," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 163-175.
    2. Jacek B. Krawczyk, 2000. "A Markovian Approximated Solution To A Portfolio Management Problem," Computing in Economics and Finance 2000 233, Society for Computational Economics.
    3. Kurt Marti, 2015. "Stochastic Optimal Open-Loop Feedback Control," Springer Books, in: Stochastic Optimization Methods, edition 3, chapter 0, pages 79-118, Springer.
    4. Kortas, Imen & Sakly, Anis & Mimouni, Mohamed Faouzi, 2015. "Analytical solution of optimized energy consumption of Double Star Induction Motor operating in transient regime using a Hamilton–Jacobi–Bellman equation," Energy, Elsevier, vol. 89(C), pages 55-64.
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