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| 摘要: |
| 本文研究两个竞争保险公司之间的非零和随机微分博弈问题. 每个保险公司可以购买再保险来降低索赔风险, 并且可以投资于一个包含无风险资产、风险资产和一个可违约债券的金融市场, 风险资产由 CEV 模型描述. 每个保险公司的目标是最大化关于竞争对手的相对终端财富的期望指数效用. 运用博弈和随机动态规划技巧, 推导出违约前和违约后的纳什均衡策略和相应的值函数. 最后对纳什均衡策略进行参数分析, 并给出经济解释. |
| 关键词: 非零和随机微分博弈 相对绩效 CEV模型 可违约风险 |
| DOI： |
| 分类号:O211.6;~O29 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| Time-consistent reinsurance and investment game with default risk under CEV model |
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liguozhu
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| Abstract: |
| This paper studies the non-zero-sum stochastic differential game between two competing insurance companies. Each insurance company can buy reinsurance to reduce the risk of claims, and can invest in a financial market that includes a risk-free asset, a defaultable bond and a risk asset satisfied a constant elasticity of variance (CEV) model. The objective of each insurer is to maximize the expected exponential utility of his terminal surplus relative to that of his competitor. Applying game theory and stochastic dynamic programming techniques, we derive the closed-form expressions of the equilibrium strategies and the corresponding value functions for the post-default case and the pre-default case. Finally, we conduct some numerical examples to illustrate the impact of model parameters on the equilibrium strategies and draw some economic interpretations from these results. |
| Key words: Non-zero-sum stochastic differential game relative performance CEV model default risk |
