Time-consistent mean-variance reinsurance-investment in a jump-diffusion financial market. (4th May 2017)

• Record Type: Journal Article
• Authors: Yang, Peng
• Is Part Of: Optimization. Volume 66:Number 5(2017)
• Page Start: 737
• Page End: 758
• Publication Date: 2017-05-04
• Subjects: Time-consistency -- proportional reinsurance -- investment -- jump-diffusion process -- common shock; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1296837
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper study an optimal time-consistent reinsurance-investment strategy selection problem in a financial market with jump-diffusion risky asset, where the insurance risk model is modulated by a compound Poisson process. The aggregate claim process and the price process of risky asset are correlated by a common Poisson process. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. Since this problem is time-inconsistent, we attack it by placing the problem within a game theoretic framework and looking for subgame perfect Nash equilibrium strategy. We investigate the problem using the extended Hamilton–Jacobi–Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategy and the corresponding value functions are obtained. Numerical examples and economic significance analysis are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.