We prove the existence of an optimal feedback controller for a stochastic optimization problem constituted by a variation of the Heston model, where a stochastic input process is added in order to minimize a given performance criterion. The stochastic feedback controller is found by solving a nonlinear backward parabolic equation for which one proves the existence and uniqueness of a martingale solution.

Feedback Optimal Controllers for the Heston Model

luca di persio
;
benazzoli chiara;Barbu, Viorel
2020-01-01

Abstract

We prove the existence of an optimal feedback controller for a stochastic optimization problem constituted by a variation of the Heston model, where a stochastic input process is added in order to minimize a given performance criterion. The stochastic feedback controller is found by solving a nonlinear backward parabolic equation for which one proves the existence and uniqueness of a martingale solution.
2020
Heston model , Stochastic Control , Feedback Controller , Hamilton-Jacobi equations , Nonlinear parabolic equations
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/988314
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