A necessary condition for optimal control of initial coupled forward-backward stochastic differential equations with partial information. (English) Zbl 1291.60126
Summary: This paper is concerned with a class of optimal control problems of forward-backward stochastic differential equations. One feature of these problems is that they are in the case of partial information and state equations are coupled at initial time. In terms of a classical convex variational technique, we establish a partial information maximum principle for the foregoing optimization problems. We also work out an example of partial information linear-quadratic optimal control to illustrate the application of the theoretical results; meanwhile, we find a forward-backward stochastic differential filtering equation, which is essentially different from classical forward stochastic filtering equations.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93E20 | Optimal stochastic control |
| 93E11 | Filtering in stochastic control theory |
Keywords:
optimal control; partial information; filtering; forward-backward stochastic differential equations; maximum principleReferences:
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