Alpha-robust mean-variance reinsurance-investment strategy |
| |
| Institution: | 1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1;2. Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, PR China;3. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, PR China;1. Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, PR China;2. School of Science, Tianjin University, Tianjin 300072, PR China;3. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, PR China;1. School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China;2. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha, 410081, PR China;1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada;2. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, PR China;1. School of Statistics, East China Normal University, Shanghai 200241, PR China;2. School of Mathematical Science, Nanjing Normal University, Jiangsu 210023, PR China |
| |
| Abstract: | Inspired by the α-maxmin expected utility, we propose a new class of mean-variance criterion, called α-maxmin mean-variance criterion, and apply it to the reinsurance-investment problem. Our model allows the insurer to have different levels of ambiguity aversion (rather than only consider the extremely ambiguity-averse attitude as in the literature). The insurer can purchase proportional reinsurance and also invest the surplus in a financial market consisting of a risk-free asset and a risky asset, whose dynamics is correlated with the insurance surplus. Closed-form equilibrium reinsurance-investment strategy is derived by solving the extended Hamilton–Jacobi–Bellman equation. Our results show that the equilibrium reinsurance strategy is always more conservative if the insurer is more ambiguity-averse. When the dependence between insurance and financial risks are weak, the equilibrium investment strategy is also more conservative if the insurer is more ambiguity-averse. However, in order to diversify the portfolio, a more ambiguity-averse insurer may adopt a more aggressive investment strategy if the insurance market is very ambiguous. For an ambiguity-neutral insurer, the investment strategy is identical to the non-robust investment strategy. |
| |
| Keywords: | Robust reinsurance-investment problem Mean-variance criterion Time-consistent equilibrium strategy Lévy insurance model C61 G11 G22 |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
