Derivation of a new Merton's optimal problem presented by fractional stochastic stock price and its applications

In this article, a new model of Merton's optimal problem is derived. This derivation is based on stock price presented by fractional order stochastic differential equation. An extension of Hamilton-Jacobi-Bellman is used to transfer our proposed model to a fractional partial differential equation. As an application of our proposed model, two optimal problems are discussed and solved, analytically.This publication was made possible by NPRP grant NPRP 5-088-1-021 from the Qatar National Research Fund (a member of Qatar Foundation).Scopu