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|Paper IPM / M / 15364||
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 Mertonâs portfolio selection model,
12 is demonstrated.
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