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J. Risk Financial Manag. 2018, 11(2), 25; https://doi.org/10.3390/jrfm11020025

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

1
School of Mathematical Sciences, Nankai University, Tianjin 300071, China
2
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
*
Author to whom correspondence should be addressed.
Received: 3 April 2018 / Revised: 9 May 2018 / Accepted: 14 May 2018 / Published: 16 May 2018
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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. View Full-Text
Keywords: optimal investment; common shock; general mean-variance optimization problem; HJB equation; value function; efficient frontier optimal investment; common shock; general mean-variance optimization problem; HJB equation; value function; efficient frontier
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Tian, Y.; Sun, Z. Mean-Variance Portfolio Selection in a Jump-Diffusion Financial Market with Common Shock Dependence. J. Risk Financial Manag. 2018, 11, 25.

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