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North American Actuarial Journal Volume 8, 2004 - Issue 2
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Original Articles

Optimal Investment for an Insurer to Minimize Its Probability of Ruin

Chi Sang Liu Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong
&
Hailiang Yang A.S.A., Ph.D. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong
Pages 11-31 | Published online: 03 Jan 2013

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Han Yu, Yu Zhang & Xikui Wang. (2023) Minimization of ruin probability with joint strategies of investment and reinsurance. Communications in Statistics - Theory and Methods 52:15, pages 5451-5469.
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Xue Dong, Ximin Rong & Hui Zhao. (2023) Non-zero-sum reinsurance and investment game with non-trivial curved strategy structure under Ornstein–Uhlenbeck process. Scandinavian Actuarial Journal 2023:6, pages 565-597.
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Haili Yuan & Yijun Hu. (2023) Optimal investment strategies for an insurer with liquid constraint. Communications in Statistics - Theory and Methods 52:7, pages 2198-2214.
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Yongtao Zhang, Hui Zhao, Ximin Rong & Kai Han. (2022) Optimal investment and reinsurance problem toward joint interests of the insurer and the reinsurer under default risk. Communications in Statistics - Theory and Methods 51:19, pages 6535-6558.
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Huainian Zhu, Ming Cao & Ying Zhu. (2021) Non-zero-sum reinsurance and investment game between two mean-variance insurers under the CEV model. Optimization 70:12, pages 2579-2606.
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Michele Longo & Gabriele Stabile. (2020) Sub-optimal investment for insurers. Communications in Statistics - Theory and Methods 49:17, pages 4298-4312.
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Zhongyang Sun. (2019) Upper bounds for ruin probabilities under model uncertainty. Communications in Statistics - Theory and Methods 48:18, pages 4511-4527.
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Xu Lin, Zhu Dongjin & Zhou Yanru. (2015) Minimizing Upper Bound of Ruin Probability Under Discrete Risk Model with Markov Chain Interest Rate. Communications in Statistics - Theory and Methods 44:4, pages 810-822.
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Jingzhen Liu, Ka-Fai Cedric Yiu, Tak Kuen Siu & Wai-Ki Ching. (2013) Optimal investment-reinsurance with dynamic risk constraint and regime switching. Scandinavian Actuarial Journal 2013:4, pages 263-285.
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Robert J. Elliott & Tak Kuen Siu. (2011) A stochastic differential game for optimal investment of an insurer with regime switching. Quantitative Finance 11:3, pages 365-380.
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Zhibin Liang & Junyi Guo. (2007) Optimal Proportional Reinsurance and Ruin Probability. Stochastic Models 23:2, pages 333-350.
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S. David Promislow & VirginiaR. Young. (2005) Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift. North American Actuarial Journal 9:3, pages 110-128.
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Articles from other publishers (71)

Bingqian Cheng, Hao Wang & Lihong Zhang. (2023) Robust investment for insurers with correlation ambiguity. The Quarterly Review of Economics and Finance.
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Arash Fahim & Lingjiong Zhu. (2023) Optimal Investment in a Dual Risk Model. Risks 11:2, pages 41.
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Masoud Komunte, Christian Kasumo & Verdiana Grace Masanja. (2022) Reducing the Possibility of Ruin by Maximizing the Survival Function for the Insurance Company’s Portfolio. Journal of Mathematics 2022, pages 1-8.
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Zilan Liu, Yijun Wang, Ya Huang & Jieming Zhou. (2022) Optimal Time-Consistent Investment and Premium Control Strategies for Insurers with Constraint under the Heston Model. Mathematics 10:7, pages 1019.
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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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Yang Shen & Bin Zou. (2021) Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process. Insurance: Mathematics and Economics 97, pages 68-80.
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Shuang-sui Liu, Wen-jing Guo & Xin-le Tong. (2021) Martingale method for optimal investment and proportional reinsurance. Applied Mathematics-A Journal of Chinese Universities 36:1, pages 16-30.
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Shumei Guo, Lili Zhang, Jie Guo, Xinna Li & Jiandong Yang. (2020) The Optimal Environment Selection Strategy of Risk Model With Perturbed Diffusion. IOP Conference Series: Materials Science and Engineering 914:1, pages 012031.
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Sheng Li & Yong He. (2020) Optimal Time-Consistent Investment and Reinsurance Strategy Under Time Delay and Risk Dependent Model. Mathematical Problems in Engineering 2020, pages 1-20.
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Jingyi Cao, David Landriault & Bin Li. (2020) Optimal reinsurance-investment strategy for a dynamic contagion claim model. Insurance: Mathematics and Economics 93, pages 206-215.
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Hong Mao & Zhongkai Wen. (2019) Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer with Multi-dimensional Time-Varying Correlation. Journal of Quantitative Economics 18:1, pages 29-51.
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Guohui Guan & Zongxia Liang. (2019) Robust optimal reinsurance and investment strategies for an AAI with multiple risks. Insurance: Mathematics and Economics 89, pages 63-78.
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Anton S. Wittl. (2019) The impact of hedging on life insurance companiesDie Auswirkungen von Hedging auf Lebensversicherungsunternehmen. Zeitschrift für die gesamte Versicherungswissenschaft 108:2, pages 165-194.
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Weipeng Yuan & Shaoyong Lai. (2019) Family optimal investment strategy for a random household expenditure under the CEV model. Journal of Computational and Applied Mathematics 354, pages 1-14.
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K.C. Wong, S.C.P. Yam & J. Zeng. (2019) Mean-risk portfolio management with bankruptcy prohibition. Insurance: Mathematics and Economics 85, pages 153-172.
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Junna Bi & Jun Cai. (2019) Optimal investment–reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets. Insurance: Mathematics and Economics 85, pages 1-14.
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Christian Kasumo. (2019) Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments. Mathematical and Computational Applications 24:1, pages 21.
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Ryan Timmer, John Paul Broussard & G. Geoffrey Booth. (2018) The efficacy of life insurance company general account equity asset allocations: a safety-first perspective using vine copulas. Annals of Actuarial Science 12:2, pages 372-390.
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Xiaoqing Liang & Virginia R. Young. (2018) Minimizing the probability of ruin: Optimal per-loss reinsurance. Insurance: Mathematics and Economics 82, pages 181-190.
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Sultan Hussain & Aqsa Parvez. (2017) Wealth Investment Strategies for Insurance Companies and the Probability of Ruin. Iranian Journal of Science and Technology, Transactions A: Science 42:3, pages 1555-1561.
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Yan Wang, Yanxiang Zhao, Lei Wang, Aimin Song & Yanping Ma. (2018) Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer. Journal of Industrial & Management Optimization 14:2, pages 653-671.
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Christian Kasumo, Juma Kasozi & Dmitry Kuznetsov. (2018) On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance. Journal of Applied Mathematics 2018, pages 1-11.
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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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Ming Zhou, Kam Chuen Yuen & Chuan-cun Yin. (2017) Optimal investment and premium control in a nonlinear diffusion model. Acta Mathematicae Applicatae Sinica, English Series 33:4, pages 945-958.
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Qing-bin Meng, Xin Zhang & Jun-na Bi. (2017) On optimal proportional reinsurance and investment in a hidden Markov financial market. Acta Mathematicae Applicatae Sinica, English Series 33:1, pages 53-62.
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Lv Chen & Hailiang Yang. (2017) Optimal reinsurance and investment strategy with two piece utility function. Journal of Industrial & Management Optimization 13:2, pages 737-755.
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Teresa Czerwińska. 2017. Risk Management in Public Administration. Risk Management in Public Administration 361 388 .
Raluca Vernic. (2015) Optimal investment with a constraint on ruin for a fuzzy discrete-time insurance risk model. Fuzzy Optimization and Decision Making 15:2, pages 195-217.
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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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HUIMING ZHU, YA HUANG, JIEMING ZHOU, XIANGQUN YANG & CHAO DENG. (2016) OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT PROBLEM WITH CONSTRAINTS ON RISK CONTROL IN A GENERAL JUMP-DIFFUSION FINANCIAL MARKET. The ANZIAM Journal 57:3, pages 352-368.
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. 2016. Ruin Probabilities. Ruin Probabilities 239 253 .
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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Ming Zhou & Kam C. Yuen. (2014) PORTFOLIO SELECTION BY MINIMIZING THE PRESENT VALUE OF CAPITAL INJECTION COSTS. ASTIN Bulletin 45:1, pages 207-238.
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Wenjing Guo. (2014) Optimal portfolio choice for an insurer with loss aversion. Insurance: Mathematics and Economics 58, pages 217-222.
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Guohui Guan & Zongxia Liang. (2014) Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks. Insurance: Mathematics and Economics 55, pages 105-115.
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Olena Ragulina. 2014. Modern Stochastics and Applications. Modern Stochastics and Applications 287 300 .
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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Bilel Jarraya & Abdelfettah Bouri. (2013) Multiobjective Optimization for the Asset Allocation of European Nonlife Insurance Companies. Journal of Multi-Criteria Decision Analysis 20:3-4, pages 97-108.
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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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Hui Zhao, Ximin Rong & Jiling Cao. (2013) Optimal Investment with Multiple Risky Assets for an Insurer in an Incomplete Market. Discrete Dynamics in Nature and Society 2013, pages 1-12.
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Zhibin Liang, Kam Chuen Yuen & Ka Chun Cheung. (2011) Optimal reinsurance–investment problem in a constant elasticity of variance stock market for jump‐diffusion risk model. Applied Stochastic Models in Business and Industry 28:6, pages 585-597.
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Zhibin Liang & Junyi Guo. (2012) Optimal investment and proportional reinsurance in the Sparre Andersen model. Journal of Systems Science and Complexity 25:5, pages 926-941.
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Xin Zhang, Robert J. Elliott & Tak Kuen Siu. (2012) A Bayesian approach for optimal reinsurance and investment in a diffusion model. Journal of Engineering Mathematics 76:1, pages 195-206.
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Yan Zeng & Zhongfei Li. (2012) Optimal reinsurance-investment strategies for insurers under mean-CaR criteria. Journal of Industrial and Management Optimization 8:3, pages 673-690.
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Jingzhen Liu, Lihua Bai & Ka-Fai Cedric Yiu. (2012) Optimal investment with a value-at-risk constraint. Journal of Industrial and Management Optimization 8:3, pages 531-547.
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Robert J. Elliott & Tak Kuen Siu. (2011) An HMM approach for optimal investment of an insurer. International Journal of Robust and Nonlinear Control 22:7, pages 778-807.
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Hong Mao & Krzysztof M. Ostaszewski. (2011) Insurance pricing, reinsurance and investment decision based on the Mutual Benefit of the insurer and the customer. Insurance pricing, reinsurance and investment decision based on the Mutual Benefit of the insurer and the customer.
Zhibin Liang, Kam Chuen Yuen & Junyi Guo. (2011) Optimal proportional reinsurance and investment in a stock market with Ornstein–Uhlenbeck process. Insurance: Mathematics and Economics 49:2, pages 207-215.
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Zhibin Liang, Lihua Bai & Junyi Guo. (2010) Optimal investment and proportional reinsurance with constrained control variables. Optimal Control Applications and Methods 32:5, pages 587-608.
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Wei Wang & Junna Bi. (2011) Markov-modulated mean-variance problem for an insurer. Acta Mathematica Scientia 31:3, pages 1051-1061.
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Robert J. Elliott & Tak Kuen Siu. (2011) A BSDE approach to a risk-based optimal investment of an insurer. Automatica 47:2, pages 253-261.
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XIANG LIN & PENG YANG. (2011) OPTIMAL INVESTMENT AND REINSURANCE IN A JUMP DIFFUSION RISK MODEL. The ANZIAM Journal 52:3, pages 250-262.
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Hong-Chih Huang. (2010) Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model. Journal of Risk and Insurance 77:2, pages 451-472.
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Xin Zhang & Tak Kuen Siu. (2009) Optimal investment and reinsurance of an insurer with model uncertainty. Insurance: Mathematics and Economics 45:1, pages 81-88.
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YIPING QIAN & XIANG LIN. (2010) RUIN PROBABILITIES UNDER AN OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE POLICY IN A JUMP DIFFUSION RISK PROCESS. The ANZIAM Journal 51:1, pages 34-48.
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Qing Zhou. (2009) Optimal investment for an insurer in the Lévy market: The martingale approach. Statistics & Probability Letters 79:14, pages 1602-1607.
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Xiang Lin. (2008) Ruin theory for classical risk process that is perturbed by diffusion with risky investments. Applied Stochastic Models in Business and Industry 25:1, pages 33-44.
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Zhibin Liang & Junyi Guo. (2007) Upper bound for ruin probabilities under optimal investment and proportional reinsurance. Applied Stochastic Models in Business and Industry 24:2, pages 109-128.
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Jostein Paulsen. (2008) Ruin models with investment income. Probability Surveys 5:none.
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Zhi-bin Liang. (2007) Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion. Acta Mathematicae Applicatae Sinica, English Series 23:3, pages 477-488.
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Zengwu Wang, Jianming Xia & Lihong Zhang. (2007) Optimal investment for an insurer: The martingale approach. Insurance: Mathematics and Economics 40:2, pages 322-334.
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P. Emms & S. Haberman. (2007) Asymptotic and numerical analysis of the optimal investment strategy for an insurer. Insurance: Mathematics and Economics 40:1, pages 113-134.
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Hailiang Yang & Lihong Zhang. (2005) Optimal investment for insurer with jump-diffusion risk process. Insurance: Mathematics and Economics 37:3, pages 615-634.
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George W. Blazenko, Andrey D. Pavlov & Gary Parker. (2007) Financial Risk Theory for a Regulated Insurer. SSRN Electronic Journal.
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Hong Mao & Zhongkai Wen. (2018) Optimal Decision on Dynamic Insurance Price and Investment Portfolio of An Insurer with Multi-Dimensional Time-Varying Correlation. SSRN Electronic Journal.
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Hong Mao & Zhongkai Wen. (2017) Optimization of Investment and Reinsurance Strategy of an Insurer Based on Stochastic Differential Game and Multi-Vasicek Model. SSRN Electronic Journal.
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Arash Fahim & Lingjiong Zhu. (2015) Optimal Investment in a Dual Risk Model. 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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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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Krzysztof Ostaszewski & Hong Mao. (2011) Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer in a Competitive Market. SSRN Electronic Journal.
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