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A stochastic maximum principle for systems with jumps, with applications to finance. (English) Zbl 1106.93342

Summary: We consider a stochastic control problem with linear dynamics with jumps, convex cost criterion, and convex state constraint, in which the control enters the drift, the diffusion, and the jump coefficients. We allow these coefficients to be random, and do not impose any \(L^p\)-bounds on the control. We obtain a stochastic maximum principle for this model that provides both necessary and sufficient conditions of optimality. This is the first version of the stochastic maximum principle that covers the consumption–investment problem in which there are jumps in the price system.

MSC:

93E20 Optimal stochastic control
49K45 Optimality conditions for problems involving randomness
91G80 Financial applications of other theories
91B62 Economic growth models
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