# American Institute of Mathematical Sciences

March  2019, 9(1): 59-76. doi: 10.3934/mcrf.2019003

## Robust optimal investment and reinsurance of an insurer under Jump-diffusion models

 1 School of Mathematics, Southeast University, Nanjing, Jiangsu Province, 211189, China 2 China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China 3 Department of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong Province, 518055, China 4 Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

* Corresponding author: Xin Zhang

Received  August 2017 Revised  April 2018 Published  August 2018

Fund Project: X. Zhang is supported by the National Natural Science Foundation of China (grant nos. 11771079, 11371020). H. Meng is supported by the National Natural Science Foundation of China (grant no. 11771465), the Program for Innovation Research in Central University of Finance and Economics, and the 111 Project (grant no. B17050). J. Xiong is supported by Southern University of Science and Technology startup fund (grant No. 28/Y01286120). Y. Shen is supported by the Natural Sciences and Engineering Research Council of Canada (grant no. RGPIN-2016-05677).

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.

Citation: Xin Zhang, Hui Meng, Jie Xiong, Yang Shen. Robust optimal investment and reinsurance of an insurer under Jump-diffusion models. Mathematical Control & Related Fields, 2019, 9 (1) : 59-76. doi: 10.3934/mcrf.2019003
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##### References:
Effects of $\lambda$ on the optimal strategies $({\hat \pi}_1, {\hat \pi}_2)$ with different $\zeta$
Effects of $q$ on the optimal strategies $({\hat \pi}_1, {\hat \pi}_2)$ with different $\zeta$
Effects of $\beta_1$ on the optimal strategies $({\hat \pi}_1, {\hat \pi}_2)$ with different $\zeta$
Effects of $\beta_2$ on the optimal strategies $({\hat \pi}_1, {\hat \pi}_2)$ with different $\zeta$
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