Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 73, Issue 9, Pages 2066-2075Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2017.02.031
Keywords
Fractional Black-Scholes equation; Merton's optimal problem; Stochastic differential equation
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Funding
- NPRP grant from the Qatar National Research Fund (Qatar Foundation) [NPRP 5-088-1-021]
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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. (C) 2017 Elsevier Ltd. All rights reserved.
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