48,928 research outputs found
Infinite horizon optimal control of forward-backward stochastic differential equations with delay
We consider a problem of optimal control of an infinite horizon system
governed by forward-backward stochastic differential equations with delay.
Sufficient and necessary maximum principles for optimal control under partial
information in infinite horizon are derived. We illustrate our results by an
application to a problem of optimal consumption with respect to recursive
utility from a cash flow with delay
A maximum principle for infinite horizon delay equations
We prove a maximum principle of optimal control of stochastic delay equations
on infinite horizon. We establish first and second sufficient stochastic
maximum principles as well as necessary conditions for that problem. We
illustrate our results by an application to the optimal consumption rate from
an economic quantity
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
Stochastic Control of Memory Mean-Field Processes
By a memory mean-field process we mean the solution of a
stochastic mean-field equation involving not just the current state and
its law at time , but also the state values and
its law at some previous times . Our purpose is to
study stochastic control problems of memory mean-field processes.
- We consider the space of measures on with the
norm introduced by Agram and {\O}ksendal in
\cite{AO1}, and prove the existence and uniqueness of solutions of memory
mean-field stochastic functional differential equations.
- We prove two stochastic maximum principles, one sufficient (a verification
theorem) and one necessary, both under partial information. The corresponding
equations for the adjoint variables are a pair of \emph{(time-) advanced
backward stochastic differential equations}, one of them with values in the
space of bounded linear functionals on path segment spaces.
- As an application of our methods, we solve a memory mean-variance problem
as well as a linear-quadratic problem of a memory process
- …