ROBUST OPTIMAL INVESTMENT AND REINSURANCE OF AN INSURER UNDER JUMP-DIFFUSION MODELS
ROBUST OPTIMAL INVESTMENT AND REINSURANCE OF AN INSURER UNDER JUMP-DIFFUSION MODELS
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跳跃扩散模型下保险公司的鲁棒最优投资与再保险
DOI：
10.3934/mcrf.2019003
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发表时间：
2019
影响因子：
1.2
通讯作者：
Yang Shen
中科院分区：
文献类型：
--
作者：
Xin Zhang;Hui Meng;Jie Xiong;Yang Shen
研究了模型不确定性下的鲁棒最优投资和再保险问题。保险人的风险过程是由一个标记点过程产生的一般跳过程来模拟的。通过将一定比例的保险风险转移给再保险公司，并将盈余通过债券和股票指数投资于金融市场，保险公司的目标是在罚款的情况下最大化最小预期终端财富。利用动态规划方法，将鲁棒最优投资和再保险问题转化为投资者与市场之间的二人零和随机微分博弈。本文导出了二次罚函数情形的封闭解。
This paper studies a robust optimal investment and reinsurance problem under model uncertainty. The insurer's risk process is modeled by a general jump process generated by a marked point process. By transferring a proportion of insurance risk to a reinsurance company and investing the surplus into the financial market with a bond and a share index, the insurance company aims to maximize the minimal expected terminal wealth with a penalty. By using the dynamic programming, we formulate the robust optimal investment and reinsurance problem into a two-person, zero-sum, stochastic differential game between the investor and the market. Closed-form solutions for the case of the quadratic penalty function are derived in our paper.