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Malliavin derivative of Teugels martingales and mean-field type stochastic maximum principle
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We study the mean-field type stochastic control problem where the
dynamics is governed by a general L\’{e}vy process with
moments of all orders. For this, we introduce the power jump processes
and the related Teugels martingales and give the Malliavin derivative
with respect to Teugels martingales. We derive necessary and sufficient
conditions for optimality of our control problem in the form of a
mean-field stochastic maximum principle.
Title: Malliavin derivative of Teugels martingales and mean-field type stochastic maximum principle
Description:
We study the mean-field type stochastic control problem where the
dynamics is governed by a general L\’{e}vy process with
moments of all orders.
For this, we introduce the power jump processes
and the related Teugels martingales and give the Malliavin derivative
with respect to Teugels martingales.
We derive necessary and sufficient
conditions for optimality of our control problem in the form of a
mean-field stochastic maximum principle.
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