| Issue |
Wuhan Univ. J. Nat. Sci.
Volume 27, Number 1, March 2022
|
|
|---|---|---|
| Page(s) | 53 - 56 | |
| DOI | https://doi.org/10.1051/wujns/2022271053 | |
| Published online | 16 March 2022 | |
Mathematics
CLC number: O232;O193
An Optimal Portfolio Problem Presented by Fractional Brownian Motion and Its Applications
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
Received: 16 August 2021
We use the dynamic programming principle method to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function, and solve the optimal portfolio problem explicitly in a Black-Scholes type of market driven by fractional Brownian motion with Hurst parameter 
. The results are compared with the corresponding well-known results in the standard Black-Scholes market 
. As an application of our proposed model, two optimal problems are discussed and solved, analytically.
Key words: fractional Brownian motion / Merton’s optimal problem / stochastic differential equation
Biography: YAN Li, female, Ph. D., research direction: stochastic optimization. E-mail: 20170046@cqnu.edu.cn
Foundation item: Supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201900506)
© Wuhan University 2022
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