Advanced search
Publication Cover
Scandinavian Actuarial Journal Volume 1998, 1998 - Issue 2
Submit an article Journal homepage
323
Views
88
CrossRef citations to date
0
Altmetric
Original article

Optimal proportional reinsurance policies for diffusion models

B. Højgaard Department of Mathematics, Aalborg University, Fr. Bajersvej 7E, DK-9220, Aalborg, Denmark E-mail: [email protected]
&
M. Taksar Department of AMS, SUNY-Stony Brook, Stony Brook, NY, 11794-3600, USA E-mail: [email protected]View further author information
Pages 166-180 | Received 01 Oct 1996, Published online: 22 Dec 2011

Citations (88)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (17)

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.
Read now
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.
Read now
Mi Chen, Ming Zhou, Haiyan Liu & Kam Chuen Yuen. (2022) Optimal dividends and reinsurance with capital injection under thinning dependence. Communications in Statistics - Theory and Methods 51:16, pages 5728-5749.
Read now
Zhuo Jin, Zuo Quan Xu & Bin Zou. (2022) A perturbation approach to optimal investment, liability ratio, and dividend strategies. Scandinavian Actuarial Journal 2022:2, pages 165-188.
Read now
Ying Zhang, Yue Wang & Peimin Chen. (2021) Stochastic optimal control on impulse dividend model with stochastic returns. Optimization 70:11, pages 2401-2426.
Read now
Khaled Masoumifard & Mohammad Zokaei. (2021) Optimal dynamic reinsurance strategies in multidimensional portfolio. Stochastic Analysis and Applications 39:1, pages 1-21.
Read now
Haluk Yener. (2020) Proportional reinsurance and investment in multiple risky assets under borrowing constraint. Scandinavian Actuarial Journal 2020:5, pages 396-418.
Read now
Anouar Houmia, Maher Mejai, Brahim Benaid & Makram ben Dbabis. (2020) Optimal proportional reinsurance policies for stochastic models. Stochastic Analysis and Applications 38:2, pages 373-386.
Read now
Peimin Chen & Xiankang Luo. (2019) Stochastic optimal control on dividend policies with bankruptcy. Optimization 68:12, pages 2317-2337.
Read now
Hiroshi Shiraishi. (2016) Review of statistical actuarial risk modelling. Cogent Mathematics 3:1.
Read now
Benjamin Avanzi. (2009) Strategies for Dividend Distribution: A Review. North American Actuarial Journal 13:2, pages 217-251.
Read now
Nicole Bäuerle. (2004) Traditional versus non-traditional reinsurance in a dynamic setting. Scandinavian Actuarial Journal 2004:5, pages 355-371.
Read now
Bjarne Højgaard & Michael Taksar. (2004) Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy. Quantitative Finance 4:3, pages 315-327.
Read now
Manfred Schäl. (2004) On Discrete-Time Dynamic Programming in Insurance: Exponential Utility and Minimizing the Ruin Probability. Scandinavian Actuarial Journal 2004:3, pages 189-210.
Read now
Chi Sang Liu & Hailiang Yang. (2004) Optimal Investment for an Insurer to Minimize Its Probability of Ruin. North American Actuarial Journal 8:2, pages 11-31.
Read now
Bjarne Højgaard. (2002) Optimal Dynamic Premium Control in Non-life Insurance. Maximizing Dividend Pay-outs. Scandinavian Actuarial Journal 2002:4, pages 225-245.
Read now
Hanspeter Schmidli. (2001) Optimal Proportional Reinsurance Policies in a Dynamic Setting. Scandinavian Actuarial Journal 2001:1, pages 55-68.
Read now

Articles from other publishers (71)

Lijun Bo, Shihua Wang & Chao Zhou. (2024) A mean field game approach to optimal investment and risk control for competitive insurers. Insurance: Mathematics and Economics 116, pages 202-217.
Crossref
Shu Zhang, Peimin Chen & Chunchi Wu. (2023) Optimal dividend decisions with capital infusion in a dynamic nonterminal bankruptcy model. Review of Quantitative Finance and Accounting 62:3, pages 911-951.
Crossref
An Chen, Hong Li & Mark B. Schultze. (2023) Optimal longevity risk transfer under asymmetric information. Economic Modelling 120, pages 106179.
Crossref
Emma Kroell, Sebastian Jaimungal & Silvana M. Pesenti. (2023) Optimal Robust Reinsurance with Multiple Insurers. SSRN Electronic Journal.
Crossref
M. Azarbad, G. A. Parham & S. M. R. Alavi. (2022) Optimal multidimensional reinsurance policies under a common shock dependency structure. European Actuarial Journal 12:2, pages 559-577.
Crossref
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.
Crossref
Leonie Violetta Brinker & Hanspeter Schmidli. (2022) Optimal discounted drawdowns in a diffusion approximation under proportional reinsurance. Journal of Applied Probability 59:2, pages 527-540.
Crossref
Dalila Guerdouh, Nabil Khelfallah & Josep Vives. (2022) Optimal Control Strategies for the Premium Policy of an Insurance Firm with Jump Diffusion Assets and Stochastic Interest Rate. Journal of Risk and Financial Management 15:3, pages 143.
Crossref
Na Li & Wei Wang. (2022) Optimal Dividend and Proportional Reinsurance Strategy Under Standard Deviation Premium Principle. Bulletin of the Malaysian Mathematical Sciences Society 45:2, pages 869-888.
Crossref
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.
Crossref
Julia Eisenberg, Lukas Fabrykowski & Maren Diane Schmeck. (2021) Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Risks 9:4, pages 73.
Crossref
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.
Crossref
Wang Yue & Qu Xiaomei. (2020) Optimal dividend control of an impulse model with stochastic risk exposure. Optimal dividend control of an impulse model with stochastic risk exposure.
Abderrahim El Attar & Mostafa El Hachloufi. (2020) Optimal Proportional Reinsurance Strategy Using Dynamic Programming. International Journal of Engineering Research in Africa 49, pages 187-197.
Crossref
Ken Seng Tan, Pengyu Wei, Wei Wei & Sheng Chao Zhuang. (2020) Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle. European Journal of Operational Research 282:1, pages 345-362.
Crossref
Xin Zhang & Xiaoxiao Zheng. (2019) Optimal Investment-Reinsurance Policy with Stochastic Interest and Inflation Rates. Mathematical Problems in Engineering 2019, pages 1-14.
Crossref
Hui Meng, Pu Liao & Tak Kuen Siu. (2019) Continuous-time optimal reinsurance strategy with nontrivial curved structures. Applied Mathematics and Computation 363, pages 124585.
Crossref
Nan Zhang, Zhuo Jin, Linyi Qian & Kun Fan. (2019) Stochastic differential reinsurance games with capital injections. Insurance: Mathematics and Economics 88, pages 7-18.
Crossref
Jose Blanchet & Karthyek Murthy. (2019) Quantifying Distributional Model Risk via Optimal Transport. Mathematics of Operations Research 44:2, pages 565-600.
Crossref
Lv Chen & Yang Shen. (2018) ON A NEW PARADIGM OF OPTIMAL REINSURANCE: A STOCHASTIC STACKELBERG DIFFERENTIAL GAME BETWEEN AN INSURER AND A REINSURER. ASTIN Bulletin 48:02, pages 905-960.
Crossref
Lihua Bai, Jin Ma & Xiaojing Xing. (2017) Optimal dividend and investment problems under Sparre Andersen model. The Annals of Applied Probability 27:6.
Crossref
Lijun Bo & Shihua Wang. (2017) Optimal investment and risk control for an insurer with stochastic factor. Operations Research Letters 45:3, pages 259-265.
Crossref
Arian Cani & Stefan Thonhauser. (2016) An optimal reinsurance problem in the Cramér–Lundberg model. Mathematical Methods of Operations Research 85:2, pages 179-205.
Crossref
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.
Crossref
Bin Zou & Abel Cadenillas. (2017) Optimal Investment and Liability Ratio Policies in a Multidimensional Regime Switching Model. Risks 5:1, pages 6.
Crossref
Xiankang Luo, Peimin Chen & Jiangming Ma. (2017) The Optimal Dividend Payout Model with Terminal Values and Its Application. Mathematical Problems in Engineering 2017, pages 1-15.
Crossref
Peimin Chen & Bo Li. (2017) Classical and Impulse Stochastic Control on the Optimization of Dividends with Residual Capital at Bankruptcy. Discrete Dynamics in Nature and Society 2017, pages 1-14.
Crossref
Nan Zhang, Zhuo Jin, Shuanming Li & Ping Chen. (2016) Optimal reinsurance under dynamic VaR constraint. Insurance: Mathematics and Economics 71, pages 232-243.
Crossref
Chunxiang A & Zhongfei Li. (2015) Optimal investment and excess-of-loss reinsurance problem with delay for an insurer under Heston’s SV model. Insurance: Mathematics and Economics 61, pages 181-196.
Crossref
Bin Zou & Abel Cadenillas. (2014) Optimal investment and risk control policies for an insurer: Expected utility maximization. Insurance: Mathematics and Economics 58, pages 57-67.
Crossref
Yang Shen & Yan Zeng. (2014) Optimal investment–reinsurance with delay for mean–variance insurers: A maximum principle approach. Insurance: Mathematics and Economics 57, pages 1-12.
Crossref
Ming Zhou & Jun Cai. (2016) Optimal Dynamic Risk Control for Insurers with State-Dependent Income. Journal of Applied Probability 51:2, pages 417-435.
Crossref
Eleni E. Roumelioti, Michael A. Zazanis & Nikos E. Frangos. (2013) Sensitivity of the joint survival probability for reinsurance schemes. Mathematical Methods in the Applied Sciences 37:2, pages 289-295.
Crossref
Mi Chen, Xiaofan Peng & Junyi Guo. (2013) Optimal dividend problem with a nonlinear regular-singular stochastic control. Insurance: Mathematics and Economics 52:3, pages 448-456.
Crossref
Jingzhen Liu, Ka Fai Cedric Yiu, Ryan C. Loxton & Kok Lay Teo. (2013) Optimal Investment and Proportional Reinsurance with Risk Constraint. Journal of Mathematical Finance 03:04, pages 437-447.
Crossref
Jingzhen Liu & Ka-Fai Cedric Yiu. (2013) Optimal stochastic differential games with VaR constraints. Discrete & Continuous Dynamical Systems - B 18:7, pages 1889-1907.
Crossref
Jingfeng Xu & Ming Zhou. (2012) Optimal risk control and dividend distribution policies for a diffusion model with terminal value. Mathematical and Computer Modelling 56:7-8, pages 180-190.
Crossref
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.
Crossref
Xin Zhang & Min Song. (2012) Optimization of risk policy and dividends with fixed transaction costs under interest rate. Frontiers of Mathematics in China 7:4, pages 795-811.
Crossref
Yan Li & Guoxin Liu. (2012) Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model. Discrete Dynamics in Nature and Society 2012, pages 1-26.
Crossref
Zongxia Liang & Jianping Huang. (2011) Optimal dividend and investing control of an insurance company with higher solvency constraints. Insurance: Mathematics and Economics 49:3, pages 501-511.
Crossref
Minghua Wu, Rong Wu & Aimin Zhou. (2011) Optimal risk control policies for diffusion models with non-cheap proportional reinsurance and bankruptcy value. Journal of Systems Science and Complexity 24:5, pages 892-906.
Crossref
Zhibin Liang & Junyi Guo. (2010) Optimal combining quota-share and excess of loss reinsurance to maximize the expected utility. Journal of Applied Mathematics and Computing 36:1-2, pages 11-25.
Crossref
XIANG LIN & PENG YANG. (2011) OPTIMAL INVESTMENT AND REINSURANCE IN A JUMP DIFFUSION RISK MODEL. The ANZIAM Journal 52:3, pages 250-262.
Crossref
Yuan Haili & Hu Yijun. (2010) Optimal proportional reinsurance with constant dividend barrier. Acta Mathematica Scientia 30:3, pages 791-798.
Crossref
Michael Taksar. 2010. Encyclopedia of Quantitative Finance. Encyclopedia of Quantitative Finance.
Tao Jiang & Liyan Wen. (2009) Ruin Probability in the Presence of Risky Investment by Insurance Capital. Ruin Probability in the Presence of Risky Investment by Insurance Capital.
Yuping Liu & Jin Ma. (2009) Optimal reinsurance/investment problems for general insurance models. The Annals of Applied Probability 19:4.
Crossref
Xin-Li Zhang, Ke-Cun Zhang & Xing-Jiang Yu. (2009) Optimal proportional reinsurance and investment with transaction costs, I: Maximizing the terminal wealth. Insurance: Mathematics and Economics 44:3, pages 473-478.
Crossref
Lin He & Zongxia Liang. (2009) Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs. Insurance: Mathematics and Economics 44:1, pages 88-94.
Crossref
Lin He, Ping Hou & Zongxia Liang. (2008) Optimal control of the insurance company with proportional reinsurance policy under solvency constraints. Insurance: Mathematics and Economics 43:3, pages 474-479.
Crossref
Lin He & Zongxia Liang. (2008) Optimal financing and dividend control of the insurance company with proportional reinsurance policy. Insurance: Mathematics and Economics 42:3, pages 976-983.
Crossref
Shangzhen Luo. (2008) Ruin Minimization for Insurers with Borrowing Constraints. North American Actuarial Journal 12:2, pages 143-174.
Crossref
Shangzhen Luo, Michael Taksar & Allanus Tsoi. (2008) On reinsurance and investment for large insurance portfolios. Insurance: Mathematics and Economics 42:1, pages 434-444.
Crossref
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.
Crossref
Michael Taksar & Christine Loft Hunderup. (2007) The influence of bankruptcy value on optimal risk control for diffusion models with proportional reinsurance. Insurance: Mathematics and Economics 40:2, pages 311-321.
Crossref
Michael Taksar. (2006) Ruin Probability Minimization and Dividend Distribution Optimization in Diffusion Models. Ruin Probability Minimization and Dividend Distribution Optimization in Diffusion Models.
Abel Cadenillas, Tahir Choulli, Michael Taksar & Lei Zhang. (2006) CLASSICAL AND IMPULSE STOCHASTIC CONTROL FOR THE OPTIMIZATION OF THE DIVIDEND AND RISK POLICIES OF AN INSURANCE FIRM. Mathematical Finance 16:1, pages 181-202.
Crossref
Hailiang Yang & Lihong Zhang. (2005) Optimal investment for insurer with jump-diffusion risk process. Insurance: Mathematics and Economics 37:3, pages 615-634.
Crossref
Marek Kaluszka. (2015) Truncated Stop Loss as Optimal Reinsurance Agreement in One-period Models. ASTIN Bulletin 35:2, pages 337-349.
Crossref
Tahir Choulli, Michael Taksar & Xun Yu Zhou. (2004) Interplay between dividend rate and business constraints for a financial corporation. The Annals of Applied Probability 14:4.
Crossref
Christian Irgens & Jostein Paulsen. (2004) Optimal control of risk exposure, reinsurance and investments for insurance portfolios. Insurance: Mathematics and Economics 35:1, pages 21-51.
Crossref
Nicole Bäuerle. (2003) Approximation of Optimal Reinsurance and Dividend Payout Policies. Mathematical Finance 14:1, pages 99-113.
Crossref
Tahir Choulli, Michael Taksar & Xun Yu Zhou. (2003) A Diffusion Model for Optimal Dividend Distribution for a Company with Constraints on Risk Control. SIAM Journal on Control and Optimization 41:6, pages 1946-1979.
Crossref
Christian Hipp & Michael Plum. (2000) Optimal investment for insurers. Insurance: Mathematics and Economics 27:2, pages 215-228.
Crossref
Christian Hipp & Michael Taksar. (2000) Stochastic control for optimal new business. Insurance: Mathematics and Economics 26:2-3, pages 185-192.
Crossref
M.I. Taksar & Xun Yu Zhou. (1997) Reinsurance and dividend policies for companies with debts. Reinsurance and dividend policies for companies with debts.
Jose Blanchet & Karthyek Murthy. (2016) Quantifying Distributional Model Risk Via Optimal Transport. SSRN Electronic Journal.
Crossref
Haluk Yener. (2015) Proportional Reinsurance and Investment in Multiple Risky Assets Under Borrowing Constraints. SSRN Electronic Journal.
Crossref
Michael I. Taksar. (2000) Optimal Risk/Dividend Distribution Control Models: Applications to Insurance. SSRN Electronic Journal.
Crossref
Benjamin Avanzi. (2008) A Review of Modern Collective Risk Theory with Dividend Strategies. SSRN Electronic Journal.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.