1,943 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
Deep combinatorial optimisation for optimal stopping time problems : application to swing options pricing
A new method for stochastic control based on neural networks and using
randomisation of discrete random variables is proposed and applied to optimal
stopping time problems. The method models directly the policy and does not need
the derivation of a dynamic programming principle nor a backward stochastic
differential equation. Unlike continuous optimization where automatic
differentiation is used directly, we propose a likelihood ratio method for
gradient computation. Numerical tests are done on the pricing of American and
swing options. The proposed algorithm succeeds in pricing high dimensional
American and swing options in a reasonable computation time, which is not
possible with classical algorithms
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