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Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin

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Cited by:

  1. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
  2. Stefan Ankirchner & Christophette Blanchet-Scalliet & Nabil Kazi-Tani & Chao Zhou, 2019. "Gambling for resurrection and the heat equation on a triangle," Working Papers hal-02405853, HAL.
  3. Moshe A. Milevsky & Kristen S. Moore & Virginia R. Young, 2006. "Asset Allocation And Annuity‐Purchase Strategies To Minimize The Probability Of Financial Ruin," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 647-671, October.
  4. Yuen, Kam Chuen & Liang, Zhibin & Zhou, Ming, 2015. "Optimal proportional reinsurance with common shock dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 1-13.
  5. Li, Zhongfei & Zeng, Yan & Lai, Yongzeng, 2012. "Optimal time-consistent investment and reinsurance strategies for insurers under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 191-203.
  6. Bayraktar, Erhan & Young, Virginia R., 2007. "Minimizing the probability of lifetime ruin under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 196-221, July.
  7. Gu, Ailing & Guo, Xianping & Li, Zhongfei & Zeng, Yan, 2012. "Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 674-684.
  8. Hipp, Christian & Plum, Michael, 2000. "Optimal investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 215-228, October.
  9. Junna Bi & Jun Cai & Yan Zeng, 2021. "Equilibrium reinsurance-investment strategies with partial information and common shock dependence," Annals of Operations Research, Springer, vol. 307(1), pages 1-24, December.
  10. Tan, Ken Seng & Wei, Pengyu & Wei, Wei & Zhuang, Sheng Chao, 2020. "Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle," European Journal of Operational Research, Elsevier, vol. 282(1), pages 345-362.
  11. Guohui Guan & Zongxia Liang & Yilun Song, 2022. "A Stackelberg reinsurance-investment game under $\alpha$-maxmin mean-variance criterion and stochastic volatility," Papers 2212.14327, arXiv.org.
  12. De-Lei Sheng & Linfeng Shi & Danping Li & Yanping Zhao, 2022. "Manage Pension Deficit with Heterogeneous Insurance," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1119-1141, June.
  13. Sona Kilianova & Daniel Sevcovic, 2013. "Transformation Method for Solving Hamilton-Jacobi-Bellman Equation for Constrained Dynamic Stochastic Optimal Allocation Problem," Papers 1307.3672, arXiv.org, revised Jul 2013.
  14. Jarraya, Bilel & Bouri, Abdelfettah, 2013. "Multiobjective optimization for the asset allocation of European nonlife insurance companies," MPRA Paper 53697, University Library of Munich, Germany, revised 2013.
  15. Derrick Huang, C. & Hu, Qing & Behara, Ravi S., 2008. "An economic analysis of the optimal information security investment in the case of a risk-averse firm," International Journal of Production Economics, Elsevier, vol. 114(2), pages 793-804, August.
  16. Begoña Fernández & Daniel Hernández-Hernández & Ana Meda & Patricia Saavedra, 2008. "An optimal investment strategy with maximal risk aversion and its ruin probability," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 159-179, August.
  17. Yao, Jing-Shing & Chen, Miao-Sheng & Lu, Huei-Fu, 2006. "A fuzzy stochastic single-period model for cash management," European Journal of Operational Research, Elsevier, vol. 170(1), pages 72-90, April.
  18. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
  19. Azcue, Pablo & Muler, Nora, 2009. "Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 26-34, February.
  20. Ya Huang & Xiangqun Yang & Jieming Zhou, 2017. "Robust optimal investment and reinsurance problem for a general insurance company under Heston model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 305-326, April.
  21. Bai, Lihua & Guo, Junyi, 2008. "Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 968-975, June.
  22. Shen, Yang & Zeng, Yan, 2015. "Optimal investment–reinsurance strategy for mean–variance insurers with square-root factor process," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 118-137.
  23. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
  24. Sheng Delei & Xing Linfang, 2018. "Optimal Insurance-Package and Investment Problem for an Insurer," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 85-96, February.
  25. Yu, Bosco Wing-Tong & Pang, Wan Kai & Troutt, Marvin D. & Hou, Shui Hung, 2009. "Objective comparisons of the optimal portfolios corresponding to different utility functions," European Journal of Operational Research, Elsevier, vol. 199(2), pages 604-610, December.
  26. Chen, Lv & Shen, Yang, 2019. "Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 120-137.
  27. Arash Fahim & Lingjiong Zhu, 2023. "Optimal Investment in a Dual Risk Model," Risks, MDPI, vol. 11(2), pages 1-29, February.
  28. Erhan Bayraktar & Virginia Young, 2011. "Proving regularity of the minimal probability of ruin via a game of stopping and control," Finance and Stochastics, Springer, vol. 15(4), pages 785-818, December.
  29. Liu, Guo & Jin, Zhuo & Li, Shuanming & Zhang, Jiannan, 2022. "Stochastic asset allocation and reinsurance game under contagious claims," Finance Research Letters, Elsevier, vol. 49(C).
  30. Yanfei Bai & Zhongbao Zhou & Helu Xiao & Rui Gao & Feimin Zhong, 2021. "A stochastic Stackelberg differential reinsurance and investment game with delay in a defaultable market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 341-381, December.
  31. Leonie Violetta Brinker, 2021. "Minimal Expected Time in Drawdown through Investment for an Insurance Diffusion Model," Risks, MDPI, vol. 9(1), pages 1-18, January.
  32. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
  33. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
  34. Xiang Lin, 2009. "Ruin theory for classical risk process that is perturbed by diffusion with risky investments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 33-44, January.
  35. Chen, Shumin & Li, Zhongfei & Li, Kemian, 2010. "Optimal investment-reinsurance policy for an insurance company with VaR constraint," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 144-153, October.
  36. Zhuo Jin & George Yin & Chao Zhu, 2011. "Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation," Papers 1111.2584, arXiv.org.
  37. Perry, David & Berg, M. & Posner, M. J. M., 2001. "Stochastic models for broker inventory in dealership markets with a cash management interpretation," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 23-34, August.
  38. Theodoros M. Diasakos, 2011. "A Simple Characterization of Dynamic Completeness in Continuous Time," Carlo Alberto Notebooks 211, Collegio Carlo Alberto.
  39. Yan Zhang & Peibiao Zhao & Rufei Ma, 2022. "Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with more General Dependent Claim Risks and Defaultable Risk," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2743-2777, December.
  40. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2021. "Stochastic differential investment and reinsurance games with nonlinear risk processes and VaR constraints," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 168-184.
  41. Jinzhu Li & Rong Wu, 2009. "Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utility," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 407-420, May.
  42. Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
  43. Virginia R. Young, 2004. "Pricing In An Incomplete Market With An Affine Term Structure," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 359-381, July.
  44. Yanfei Bai & Zhongbao Zhou & Helu Xiao & Rui Gao & Feimin Zhong, 2019. "A hybrid stochastic differential reinsurance and investment game with bounded memory," Papers 1910.09834, arXiv.org.
  45. Shihao Zhu & Jingtao Shi, 2019. "Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full Information," Papers 1906.08410, arXiv.org, revised Jun 2020.
  46. Erhan Bayraktar & Virginia R. Young, 2007. "Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin," Papers math/0703862, arXiv.org, revised Oct 2007.
  47. Zou, Bin & Cadenillas, Abel, 2014. "Optimal investment and risk control policies for an insurer: Expected utility maximization," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 57-67.
  48. Chang Guo & Xiaoyang Zhuo & Corina Constantinescu & Olivier Menoukeu Pamen, 2018. "Optimal Reinsurance-Investment Strategy Under Risks of Interest Rate, Exchange Rate and Inflation," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1477-1502, December.
  49. Junna Bi & Junyi Guo, 2013. "Optimal Mean-Variance Problem with Constrained Controls in a Jump-Diffusion Financial Market for an Insurer," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 252-275, April.
  50. Opler, Tim & Pinkowitz, Lee & Stulz, Rene & Williamson, Rohan, 1999. "The determinants and implications of corporate cash holdings," Journal of Financial Economics, Elsevier, vol. 52(1), pages 3-46, April.
  51. Deng, Chao & Zeng, Xudong & Zhu, Huiming, 2018. "Non-zero-sum stochastic differential reinsurance and investment games with default risk," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1144-1158.
  52. Guan, Guohui & Hu, Jiaqi & Liang, Zongxia, 2022. "Robust equilibrium strategies in a defined benefit pension plan game," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 193-217.
  53. Wang, Hao & Wang, Rongming & Wei, Jiaqin, 2019. "Time-consistent investment-proportional reinsurance strategy with random coefficients for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 104-114.
  54. Qicai Li & Mengdi Gu & Zhibing Liang, 2014. "Optimal excess-of-loss reinsurance and investment polices under the CEV model," Annals of Operations Research, Springer, vol. 223(1), pages 273-290, December.
  55. Bjarne Højgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327.
  56. Hong Mao & Zhongkai Wen, 2020. "Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer with Multi-dimensional Time-Varying Correlation," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(1), pages 29-51, March.
  57. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
  58. Zhang, Xin-Li & Zhang, Ke-Cun & Yu, Xing-Jiang, 2009. "Optimal proportional reinsurance and investment with transaction costs, I: Maximizing the terminal wealth," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 473-478, June.
  59. A, Chunxiang & Li, Zhongfei, 2015. "Optimal investment and excess-of-loss reinsurance problem with delay for an insurer under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 181-196.
  60. Ye, Jun & Li, Tiantian, 2012. "The optimal mean–variance investment strategy under value-at-risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 344-351.
  61. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
  62. J. Cerda-Hernandez & A. Sikov, 2022. "Optimal investment strategy to maximize the expected utility of an insurance company under Cramer Lundberg dynamic," Papers 2207.02947, arXiv.org.
  63. Aaron Zeff Palmer & Alexander Vladimirsky, 2017. "Optimal Stopping with a Probabilistic Constraint," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 795-817, December.
  64. Bi, Junna & Cai, Jun, 2019. "Optimal investment–reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 1-14.
  65. Caibin Zhang & Zhibin Liang & Kam Chuen Yuen, 2019. "Optimal dynamic reinsurance with common shock dependence and state-dependent risk aversion," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-45, March.
  66. Emms, P. & Haberman, S., 2007. "Asymptotic and numerical analysis of the optimal investment strategy for an insurer," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 113-134, January.
  67. Mohamed Badaoui & Begoña Fernández & Anatoliy Swishchuk, 2018. "An Optimal Investment Strategy for Insurers in Incomplete Markets," Risks, MDPI, vol. 6(2), pages 1-23, April.
  68. Meng, Hui & Li, Shuanming & Jin, Zhuo, 2015. "A reinsurance game between two insurance companies with nonlinear risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 91-97.
  69. Alia, Ishak & Chighoub, Farid & Sohail, Ayesha, 2016. "A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 212-223.
  70. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
  71. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
  72. Egami, Masahiko & Young, Virginia R., 2009. "Optimal reinsurance strategy under fixed cost and delay," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 1015-1034, March.
  73. Luo, Shangzhen & Taksar, Michael, 2011. "On absolute ruin minimization under a diffusion approximation model," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 123-133, January.
  74. Christensen, Bent Jesper & Parra-Alvarez, Juan Carlos & Serrano, Rafael, 2021. "Optimal control of investment, premium and deductible for a non-life insurance company," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 384-405.
  75. Guan, Guohui & Liang, Zongxia & Feng, Jian, 2018. "Time-consistent proportional reinsurance and investment strategies under ambiguous environment," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 122-133.
  76. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
  77. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
  78. Cao, Yusong & Wan, Nianqing, 2009. "Optimal proportional reinsurance and investment based on Hamilton-Jacobi-Bellman equation," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 157-162, October.
  79. Zhou, Jieming & Yang, Xiangqun & Guo, Junyi, 2017. "Portfolio selection and risk control for an insurer in the Lévy market under mean–variance criterion," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 139-149.
  80. Xue, Xiaole & Wei, Pengyu & Weng, Chengguo, 2019. "Derivatives trading for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 40-53.
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  82. Irgens, Christian & Paulsen, Jostein, 2004. "Optimal control of risk exposure, reinsurance and investments for insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 21-51, August.
  83. Perry, David & Stadje, Wolfgang, 2000. "Risk analysis for a stochastic cash management model with two types of customers," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 25-36, February.
  84. Bin Zou & Abel Cadenillas, 2017. "Optimal Investment and Liability Ratio Policies in a Multidimensional Regime Switching Model," Risks, MDPI, vol. 5(1), pages 1-22, January.
  85. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
  86. Stefan Ankirchner & Christophette Blanchet-Scalliet & Nabil Kazi-Tani & Chao Zhou, 2021. "Gambling for resurrection and the heat equation on a triangle," Post-Print hal-02405853, HAL.
  87. Li, Zhongfei & Yao, Jing & Li, Duan, 2010. "Behavior patterns of investment strategies under Roy's safety-first principle," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(2), pages 167-179, May.
  88. Lihua Bai & Huayue Zhang, 2008. "Dynamic mean-variance problem with constrained risk control for the insurers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 181-205, August.
  89. Landriault, David & Li, Bin & Loke, Sooie-Hoe & Willmot, Gordon E. & Xu, Di, 2017. "A note on the convexity of ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 1-6.
  90. Yan, Tingjin & Park, Kyunghyun & Wong, Hoi Ying, 2022. "Irreversible reinsurance: A singular control approach," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 326-348.
  91. Arash Fahim & Lingjiong Zhu, 2015. "Optimal Investment in a Dual Risk Model," Papers 1510.04924, arXiv.org, revised Feb 2023.
  92. Chen, Lv & Qian, Linyi & Shen, Yang & Wang, Wei, 2016. "Constrained investment–reinsurance optimization with regime switching under variance premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 253-267.
  93. Zhao, Qian & Wang, Rongming & Wei, Jiaqin, 2016. "Exponential utility maximization for an insurer with time-inconsistent preferences," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 89-104.
  94. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2020. "A Perturbation Approach to Optimal Investment, Liability Ratio, and Dividend Strategies," Papers 2012.06703, arXiv.org, revised May 2021.
  95. Junna Bi & Zhibin Liang & Kam Chuen Yuen, 2019. "Optimal mean–variance investment/reinsurance with common shock in a regime-switching market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 109-135, August.
  96. Yanfei Bai & Zhongbao Zhou & Rui Gao & Helu Xiao, 2020. "Nash Equilibrium Investment-Reinsurance Strategies for an Insurer and a Reinsurer with Intertemporal Restrictions and Common Interests," Mathematics, MDPI, vol. 8(1), pages 1-26, January.
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  123. Wujun Lv & Linlin Tian & Xiaoyi Zhang, 2023. "Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence," Mathematics, MDPI, vol. 11(13), pages 1-20, July.
  124. Zhu, Huiming & Deng, Chao & Yue, Shengjie & Deng, Yingchun, 2015. "Optimal reinsurance and investment problem for an insurer with counterparty risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 242-254.
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  128. Chen, Mi & Peng, Xiaofan & Guo, Junyi, 2013. "Optimal dividend problem with a nonlinear regular-singular stochastic control," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 448-456.
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