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

In this article, a new model of Mertons optimal problem is derived. This derivation is based on stock price presented by fractional order stochastic differential equation. An extension of HamiltonJacobiBellman 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.

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