A maximum principle for optimal control of stochastic systems with delay, with applications to finance
نویسندگان
چکیده
We consider optimal control problems for systems described by stochastic differential equations with delay. We prove two (sufficient) maximum principles for certain classes of such systems, one for ordinary stochastic delay control and one which also includes singular stochastic delay control. As an application we find explicitly the optimal consumption rate from an economic quantity described by a stochastic delay equation of a certain type. We also solve a Merton type optimal portfolio problem in a market with delay.
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