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- Title
Mean-Variance Portfolio Selection in a Jump-Diffusion Financial Market with Common Shock Dependence.
- Authors
Yingxu Tian; Zhongyang Sun
- 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.
- Subjects
INVESTMENT risk; FINANCIAL markets; HAMILTON-Jacobi-Bellman equation; PARTIAL differential equations; MATHEMATICAL optimization
- Publication
Journal of Risk & Financial Management, 2018, Vol 11, Issue 2, p1
- ISSN
1911-8066
- Publication type
Article
- DOI
10.3390/jrfm11020025