58 research outputs found
Maximum principle for a stochastic delayed system involving terminal state constraints
We investigate a stochastic optimal control problem where the controlled
system is depicted as a stochastic differential delayed equation; however, at
the terminal time, the state is constrained in a convex set. We firstly
introduce an equivalent backward delayed system depicted as a time-delayed
backward stochastic differential equation. Then a stochastic maximum principle
is obtained by virtue of Ekeland's variational principle. Finally, applications
to a state constrained stochastic delayed linear-quadratic control model and a
production-consumption choice problem are studied to illustrate the main
obtained result.Comment: 16 page
Maximum principle for a Markovian regime switching system under model uncertainty
In this paper, we study a stochastic optimal control problem with a Markovian
regime switching system, where the coefficients of the state equation and the
cost functional are uncertain. First, we obtain the variational inequality by
showing the continuity with respect to the uncertainty parameter of the
variational equation, which is characterized as forward-backward stochastic
differential equations. Second, using the linearization method and weak
convergence technique, we prove the necessary stochastic maximum principle and
show the sufficient condition of the stochastic optimal control. Finally, as an
application, a risk-minimizing portfolio selection problem is studied.
Meanwhile, the -solution and -estimate of stochastic
differential equations with regime switching are given for \b=2k with .Comment: 37 Page
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