Author： Lefebvre M.
Publisher： Taylor & Francis Ltd
ISSN： 1464-5319
Source： International Journal of Systems Science, Vol.31, Iss.10, 2000-10, pp. : 1317-1322
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Abstract
Let x(t) = (x1(t), xx(t)2) be defined by the stochastic differential equations dxi(t) = ai[x(t)]dt +σ2j=1 bij [x(t)]uj(t)dt + c 1/2i[x(t)]d Wi(t), where Wi is a standard Brownian motion, for i = 1,2. There are two optimizers. The first one, using u1(t), tries to minimize the expected value of a quadratic cost criterion J, while the second one, using u(t), wants to maximize this expected value. The game ends the first time x(t) reaches a subset of IR2. It is shown that it is sometimes possible to linearize the dynamic programming equation that must be solved to obtain the optimal value of ui(t). Examples are solved explicitly.
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