TY - JOUR
T1 - The State Equations Methods for Stochastic Control Problems
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 79
EP - 96
PY - 2010
DA - 2010/03
SN - 3
DO - http://doi.org/10.4208/nmtma.2009.m99006
UR - https://global-sci.org/intro/article_detail/nmtma/5990.html
KW - Stochastic optimal control, Markov chain approximation, Euler-Maruyama discretisation, midpoint rule, predictor-corrector methods, portfolio management.
AB - <p style="text-align: justify;">The state equations of stochastic control problems, which are
controlled stochastic differential equations, are proposed to be
discretized by the weak midpoint rule and predictor-corrector
methods for the Markov chain approximation approach. Local
consistency of the methods are proved. Numerical tests on a
simplified Merton&#39;s portfolio model show better simulation to
feedback control rules by these two methods, as compared with the
weak Euler-Maruyama discretisation used by Krawczyk. This suggests a
new approach of improving accuracy of approximating Markov chains
for stochastic control problems.</p>