Mean-Variance Portfolio Selection in a Jump-Diffusion Financial Market with Common Shock Dependence

Yingxu Tian and Zhongyang Sun
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Yingxu Tian: School of Mathematical Sciences, Nankai University, Tianjin 300071, China
Zhongyang Sun: School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

JRFM, 2018, vol. 11, issue 2, 1-12

Abstract: This paper considers the optimal investment problem in a financial market with one risk-free asset and one jump-diffusion risky asset. It is assumed that the insurance risk process is driven by a compound Poisson process and the two jump number processes are correlated by a common shock. A general mean-variance optimization problem is investigated, that is, besides the objective of terminal condition, the quadratic optimization functional includes also a running penalizing cost, which represents the deviations of the insurer’s wealth from a desired profit-solvency goal. By solving the Hamilton-Jacobi-Bellman (HJB) equation, we derive the closed-form expressions for the value function, as well as the optimal strategy. Moreover, under suitable assumption on model parameters, our problem reduces to the classical mean-variance portfolio selection problem and the efficient frontier is obtained.

Keywords: optimal investment; common shock; general mean-variance optimization problem; HJB equation; value function; efficient frontier (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2018
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