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North American Actuarial Journal Volume 15, 2011 - Issue 3
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Original Articles

Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model

Xiang Lin CAA, PhD School of Mathematics, Central South University, No. 22 South Shaoshan Road, Changsha 410075, Hunan, China E-mail: [email protected]
&
Yanfang Li School of Mathematics, Henan Polytechnic University, No. 2001 Century Avenue, Jiaozuo 454000, Henan, China
Pages 417-431 | Published online: 27 Dec 2012

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Ximin Rong, Yiqi Yan & Hui Zhao. (2023) Asymptotic solution of optimal reinsurance and investment problem with correlation risk for an insurer under the CEV model. International Journal of Control 96:4, pages 840-853.
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Hao Chang & Jiaao Li. (2023) Robust equilibrium strategy for DC pension plan with the return of premiums clauses in a jump-diffusion model. Optimization 72:2, pages 463-492.
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Hao Chang, Xueyan Li & Xingjiang Chen. (2022) Optimal consumption and portfolios with the hyperbolic absolute risk aversion preference under the CEV model. Communications in Statistics - Theory and Methods 51:24, pages 8799-8821.
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Yong He, Kaili Xiang, Peimin Chen & Chunchi Wu. (2022) Optimal investment strategy with constant absolute risk aversion utility under an extended CEV model. Optimization 71:15, pages 4571-4601.
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Guohui Guan & Xiang Hu. (2022) Time-Consistent Investment and Reinsurance Strategies for Mean–Variance Insurers in N-Agent and Mean-Field Games. North American Actuarial Journal 26:4, pages 537-569.
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Danping Li, Xiaotao Liu & Hailong Liu. (2022) Optimal investment strategy for a family with a random household expenditure under the CEV model. Communications in Statistics - Theory and Methods 51:17, pages 5993-6007.
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Yingchun Deng, Man Li, Ya Huang & Jieming Zhou. (2021) Robust optimal strategies for an insurer under generalized mean-variance premium principle with defaultable bond. Communications in Statistics - Theory and Methods 50:21, pages 5126-5159.
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Danping Li, Yongzeng Lai & Lin Li. (2020) Optimal asset allocation with heterogeneous discounting and stochastic income under CEV model. Journal of the Operational Research Society 71:12, pages 2013-2026.
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Guohui Guan & Xiaojun Wang. (2020) Time-consistent reinsurance and investment strategies for an AAI under smooth ambiguity utility. Scandinavian Actuarial Journal 2020:8, pages 677-699.
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Dengfeng Xia, Weijie Yuan & Weiyin Fei. (2019) Optimal reinsurance and investment for an insurer with the jump diffusion risk model in A-C case. Systems Science & Control Engineering 7:3, pages 13-19.
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Suxin Wang, Ximin Rong & Hui Zhao. (2019) Mean-variance problem for an insurer with default risk under a jump-diffusion risk model. Communications in Statistics - Theory and Methods 48:17, pages 4221-4249.
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Qiang Zhang & Ping Chen. (2018) Time-consistent mean–variance proportional reinsurance and investment problem in a defaultable market. Optimization 67:5, pages 683-699.
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Danping Li, Yan Zeng & Hailiang Yang. (2018) Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps. Scandinavian Actuarial Journal 2018:2, pages 145-171.
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Peng Yang. (2017) Time-consistent mean-variance reinsurance-investment in a jump-diffusion financial market. Optimization 66:5, pages 737-758.
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Shangzhen Luo, Mingming Wang & Xudong Zeng. (2016) Optimal reinsurance: minimize the expected time to reach a goal. Scandinavian Actuarial Journal 2016:8, pages 741-762.
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Xiang Lin & Yiping Qian. (2016) Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model. Scandinavian Actuarial Journal 2016:7, pages 646-671.
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Yang Yang, Guojing Wang & Jing Yao. (2024) Time-consistent reinsurance-investment games for multiple mean-variance insurers with mispricing and default risks. Insurance: Mathematics and Economics 114, pages 79-107.
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Ning Bin, Huainian Zhu & Chengke Zhang. (2023) Stochastic Differential Games on Optimal Investment and Reinsurance Strategy with Delay Under the CEV Model. Methodology and Computing in Applied Probability 25:2.
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Yong He, Peimin Chen, Lin He, Kaili Xiang & Chunchi Wu. (2023) A dynamic Heston local–stochastic volatility model and Legendre transform dual-asymptotic solution for optimal investment strategy problems with CARA utility. Journal of Computational and Applied Mathematics 423, pages 114993.
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Wuyuan Jiang & Zhaojun Yang. (2023) Optimal robust reinsurance contracts with investment strategy under variance premium principle. Mathematical Control and Related Fields 0:0, pages 0-0.
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Yan Zhang, Peibiao Zhao & Huaren Zhou. (2022) The Optimal Reinsurance-Investment Problem Considering the Joint Interests of an Insurer and a Reinsurer under Hara Utility. Acta Mathematica Scientia 43:1, pages 97-124.
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Yong He, Xia Zhou, Peimin Chen & Xiaoyang Wang. (2022) An analytical solution for the robust investment-reinsurance strategy with general utilities. The North American Journal of Economics and Finance 63, pages 101789.
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Yan Zhang & Peibiao Zhao. (2022) Asymptotic Behavior of an Optimal Investment-Reinsurance Problem with General Utility Functions. Discrete Dynamics in Nature and Society 2022, pages 1-18.
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Xia Zhou, Peimin Chen, Jiawei Zhang, Jingwen Tu & Yong He. (2022) The optimal investment-reinsurance strategies for ambiguity aversion insurer in uncertain environment. Journal of Industrial and Management Optimization 0:0, pages 0.
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Shan Liu, Hui Zhao & Ximin Rong. (2022) Time-consistent investment-reinsurance strategy with a defaultable security under ambiguous environment. Journal of Industrial & Management Optimization 18:2, pages 1185.
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Chun-Xiang A, Ai-Lin Gu & Yi Shao. (2021) Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model. Journal of the Operations Research Society of China 9:2, pages 245-271.
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Yan Zhang, Peibiao Zhao, Xinghu Teng & Lei Mao. (2021) Optimal reinsurance and investment strategies for an insurer and a reinsurer under Hestons SV model: HARA utility and Legendre transform. Journal of Industrial & Management Optimization 17:4, pages 2139.
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Jiaqi Zhu, Guohui Guan & Shenghong Li. (2020) Time-consistent non-zero-sum stochastic differential reinsurance and investment game under default and volatility risks. Journal of Computational and Applied Mathematics 374, pages 112737.
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Peng Yang. (2020) Robust Time-Consistent Portfolio Selection for an Investor under CEV Model with Inflation Influence. Mathematical Problems in Engineering 2020, pages 1-14.
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Qiang Zhang & Ping Chen. (2019) Optimal Reinsurance and Investment Strategy for an Insurer in a Model with Delay and Jumps. Methodology and Computing in Applied Probability 22:2, pages 777-801.
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Xiaotao Liu & Hailong Liu. (2020) Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process. Mathematical Problems in Engineering 2020, pages 1-10.
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Danping Li, Ruiqing Chen & Cunfang Li. (2020) Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation. Mathematical Problems in Engineering 2020, pages 1-19.
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Yong He & Peimin Chen. (2020) Optimal Investment Strategy under the CEV Model with Stochastic Interest Rate. Mathematical Problems in Engineering 2020, pages 1-11.
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Hui Zhao, Yang Shen, Yan Zeng & Wenjun Zhang. (2019) Robust equilibrium excess-of-loss reinsurance and CDS investment strategies for a mean–variance insurer with ambiguity aversion. Insurance: Mathematics and Economics 88, pages 159-180.
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Qiang Zhang & Ping Chen. (2019) Robust optimal proportional reinsurance and investment strategy for an insurer with defaultable risks and jumps. Journal of Computational and Applied Mathematics 356, pages 46-66.
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Xiaole Xue, Pengyu Wei & Chengguo Weng. (2019) Derivatives trading for insurers. Insurance: Mathematics and Economics 84, pages 40-53.
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Guohui Guan, Zongxia Liang & Jian Feng. (2018) Time-consistent proportional reinsurance and investment strategies under ambiguous environment. Insurance: Mathematics and Economics 83, pages 122-133.
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Chunxiang A, Yongzeng Lai & Yi Shao. (2018) Optimal excess-of-loss reinsurance and investment problem with delay and jump–diffusion risk process under the CEV model. Journal of Computational and Applied Mathematics 342, pages 317-336.
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Yajie Wang, Ximin Rong & Hui Zhao. (2018) Optimal investment strategies for an insurer and a reinsurer with a jump diffusion risk process under the CEV model. Journal of Computational and Applied Mathematics 328, pages 414-431.
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Hui Zhao & Ximin Rong. (2017) On the constant elasticity of variance model for the utility maximization problem with multiple risky assets. IMA Journal of Management Mathematics 28:2, pages 299-320.
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Hui Zhao, ChengGuo Weng, Yang Shen & Yan Zeng. (2016) Time-consistent investment-reinsurance strategies towards joint interests of the insurer and the reinsurer under CEV models. Science China Mathematics 60:2, pages 317-344.
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Danping Li, Ximin Rong & Hui Zhao. (2014) Optimal reinsurance and investment problem for an insurer and a reinsurer with jump-diffusion risk process under the Heston model. Computational and Applied Mathematics 35:2, pages 533-557.
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Hui Zhao, Yang Shen & Yan Zeng. (2016) Time-consistent investment-reinsurance strategy for mean-variance insurers with a defaultable security. Journal of Mathematical Analysis and Applications 437:2, pages 1036-1057.
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Danping Li, Ximin Rong & Hui Zhao. (2016) The optimal investment problem for an insurer and a reinsurer under the constant elasticity of variance model. IMA Journal of Management Mathematics 27:2, pages 255-280.
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Xiaoxiao Zheng, Jieming Zhou & Zhongyang Sun. (2016) Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model. Insurance: Mathematics and Economics 67, pages 77-87.
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Cristina Gosio, Ester C. Lari & Marina Ravera. (2016) Optimal Dynamic Proportional and Excess of Loss Reinsurance under Dependent Risks. Modern Economy 07:06, pages 715-724.
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Jingyun Sun, Zhongfei Li & Yongwu Li. (2016) Equilibrium Investment Strategy for DC Pension Plan with Inflation and Stochastic Income under Heston’s SV Model. Mathematical Problems in Engineering 2016, pages 1-18.
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Danping Li, Ximin Rong & Hui Zhao. (2015) Optimal investment problem for an insurer and a reinsurer. Journal of Systems Science and Complexity 28:6, pages 1326-1343.
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Danping Li, Ximin Rong & Hui Zhao. (2015) Time-consistent reinsurance–investment strategy for a mean–variance insurer under stochastic interest rate model and inflation risk. Insurance: Mathematics and Economics 64, pages 28-44.
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Yang Shen & Yan Zeng. (2015) Optimal investment–reinsurance strategy for mean–variance insurers with square-root factor process. Insurance: Mathematics and Economics 62, pages 118-137.
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Jieming ZHOU, Yingchun DENG, Ya HUANG & Xiangqun YANG. (2015) Optimal proportional reinsurance and investment for a constant elasticity of variance model under variance principle. Acta Mathematica Scientia 35:2, pages 303-312.
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Cristina Gosio, Ester C. Lari & Marina Ravera. (2015) Optimal Proportional Reinsurance in a Bivariate Risk Model. Modern Economy 06:06, pages 664-671.
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Hao Chang & Kai Chang. (2014) Legendre transform-dual solution for investment and consumption problem under the Vasicek model. Journal of Systems Science and Complexity 27:5, pages 911-927.
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De-Lei Sheng, Ximin Rong & Hui Zhao. (2014) Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions. Abstract and Applied Analysis 2014, pages 1-19.
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Hui Zhao, Ximin Rong & Yonggan Zhao. (2013) Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model. Insurance: Mathematics and Economics 53:3, pages 504-514.
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Hong Mao, James M. Carson, Krzysztof M. Ostaszewski & Zhongkai Wen. (2013) Optimal decision on dynamic insurance price and investment portfolio of an insurer. Insurance: Mathematics and Economics 52:2, pages 359-369.
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Chi-Fai Lo. (2013) The Sum and Difference of Two Constant Elasticity of Variance Stochastic Variables. Applied Mathematics 04:11, pages 1503-1511.
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Ailing Gu, Xianping Guo, Zhongfei Li & Yan Zeng. (2012) Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model. Insurance: Mathematics and Economics 51:3, pages 674-684.
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Xiaotao Liu & Hailong Liu. (2018) Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model. SSRN Electronic Journal.
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Hui Zhao, Yang Shen, Yan Zeng & Wenjun Zhang. (2018) Robust Equilibrium Excess-of-Loss Reinsurance and CDS Investment Strategies for a Mean-Variance Insurer with Ambiguity Aversion. SSRN Electronic Journal.
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Xiaole Xue, Pengyu Wei & Chengguo Weng. (2018) Derivatives Trading for Insurers. SSRN Electronic Journal.
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Hui Zhao, Yang Shen & Yan Zeng. (2014) Time-Consistent Investment-Reinsurance Strategy for Mean-Variance Insurers With a Defaultable Security. SSRN Electronic Journal.
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Hui Zhao, Chengguo Weng & Yan Zeng. (2014) Time-Consistent Investment-Reinsurance Strategies Towards Joint Interests of the Insurer and the Reinsurer Under CEV Models. SSRN Electronic Journal.
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C.F. Lo. (2013) The Sum and Difference of Two Constant Elasticity of Variance Stochastic Variables. SSRN Electronic Journal.
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Krzysztof Ostaszewski & Hong Mao. (2011) Determining the Optimal Investment and Reinsurance Strategy of Insurance Company Based on Stochastic Differential Game. SSRN Electronic Journal.
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