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STOCHASTIC HAMILTON-JACOBI-BELLMAN EQUATION AND VISCOSITY SOLUTIONS IN THE CASE OF MAXIMIZING THE EXPECTATION OF THE UTILITY FUNCTION OF THE FRACTIONAL BLACK-SCHOLES MODEL APPROXIMATED BY A SEMIMARTINGALE
Keywords:
optimal stochastic control, stochastic Hamilton-Jacobi-Bellman equation, viscosity solution, semimartingaleDOI:
https://doi.org/10.17654/0972086323003Abstract
In this paper, we establish Hamilton-Jacobi-Bellman (HJB) equation for the fractional Black-Scholes model approximated by a semimartingale. We show the existence and the uniqueness of a viscosity type solution for the HJB equation associated to this problem.
Received: November 2, 2022; Accepted: January 3, 2023; Published: January 13, 2023
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