Equilibrium dividend strategies for spectrally negative Lévy processes with time value of ruin and random time horizon

References

• Asmussen, S., and M. Taksar. 1997. Controlled diffusion models for optimal dividend pay-out. Insurance: Mathematics and Economics 20 (1):1–15.
   Web of Science ®Google Scholar
• Applebaum, D. 2009. Lévy processes and stochastic calculus. 2nd ed. Cambridge, UK: Cambridge university Press.
   Google Scholar
• Avram, F., Z. Palmowski, and R. P. Martijn. 2007. On the optimal dividend problem for a spectrally negative Lévy process. The Annals of Applied Probability 17 (1):156–80.
   Web of Science ®Google Scholar
• Bertoin, J. 1996. Lévy processes. Cambridge Tracts in Mathematics. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Björk, T., and A. Murgoci. 2010. A general theory of Markovian time inconsistent stochastic control problems. Working paper, Stockholm School of Economics.
   Google Scholar
• Björk, T., M. Khapko, and A. Murgoci. 2017. On time-inconsistent stochastic control in continuous time. Finance and Stochastics 21 (2):331–60.
   Web of Science ®Google Scholar
• Chen, S., Y. Zeng, and Z. Hao. 2017. Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramér-Lundberg model. Insurance: Mathematics and Economics 74:31–45.
   Web of Science ®Google Scholar
• Chen, S., Z. Li, and Y. Zeng. 2018. Optimal dividend strategy for a general diffusion process with time-inconsistent preferences and ruin penalty. SIAM Journal on Financial Mathematics 9 (1):274–314.
   Web of Science ®Google Scholar
• Dong, H., C. Yin, and H. Dai. 2019. Spectrally negative Lévy risk model under Erlangized barrier strategy. Journal of Computational and Applied Mathematics 351:101–16.
   Web of Science ®Google Scholar
• Ekeland, I., O. Mbodji, and T. A. Pirvu. 2012. Time-consistent portfolio management. SIAM Journal on Financial Mathematics 3 (1):1–32.
   Web of Science ®Google Scholar
• Ekeland, I., and T. A. Pirvu. 2008. Investment and consumption without commitment. Mathematics and Financial Economics 2 (1):57–86.
   Web of Science ®Google Scholar
• Gerber, H. U., and E. S. Shiu. 2006. On optimal dividend strategies in the compound Poisson model. North American Actuarial Journal 10 (2):76–93.
   Google Scholar
• Klebaner, F. C. 2012. Introduction to stochastic calculus with applications. 3rd ed. Singapore: World Scientific Publishing Company.
   Google Scholar
• Kyprianou, A. E., R. Loeffen, and J. L. Pérez. 2012. Optimal control with absolutely continuous strategies for spectrally negative Lévy processes. Journal of Applied Probability 49 (1):150–66.
   Web of Science ®Google Scholar
• Li, M., and G. Yin. 2019. Optimal threshold strategies with capital injections in a spectrally negative Lévy risk model. Journal of Industrial & Management Optimization 15 (2):517–35.
   Web of Science ®Google Scholar
• Li, Y., Z. Li, and Y. Zeng. 2016. Equilibrium dividend strategy with non-exponential discounting in a dual model. Journal of Optimization Theory and Applications 168 (2):699–722.
   Web of Science ®Google Scholar
• Marín-Solano, J., and J. Navas. 2010. Consumption and portfolio rules for time-inconsistent investors. European Journal of Operational Research 201 (3):860–72.
   Web of Science ®Google Scholar
• Strotz, R. H. 1955. Myopia and inconsistency in dynamic utility maximization. The Review of Economic Studies 23 (3):165–80.
   Web of Science ®Google Scholar
• Thaler, R. H. 1981. Some empirical evidence on dynamic inconsistency. Economics Letters 8 (3):201–207.
   Web of Science ®Google Scholar
• Thonhauser, S., and H. Albrecher. 2007. Dividend maximization under consideration of the time value of ruin. Insurance: Mathematics and Economics 41 (1):163–84.
   Web of Science ®Google Scholar
• Wang, T., Z. Jin, and J. Wei. 2019. Mean-variance portfolio selection under a non-Markovian regime-switching model: Time-consistent solutions. SIAM Journal on Control and Optimization 57 (5):3249–71.
   Web of Science ®Google Scholar
• Wei, J., and T. Wang. 2017. Time-consistent meanCvariance asset-liability management with random coefficients. Insurance: Mathematics and Economics 77:84–96.
   Web of Science ®Google Scholar
• Yin, C., Y. Wen, and Y. Zhao. 2014. On the optimal dividend problem for a spectrally positive Lévy process. ASTIN Bulletin 44 (3):635–51.
   Web of Science ®Google Scholar
• Yong, J. 2012. Time-inconsistent optimal control problems and the equilibrium HJB-equation. Mathematical Control & Related Fields 2 (3):271–329.
   Web of Science ®Google Scholar
• Zeng, Y., and Z. Li. 2011. Optimal time-consistent investment and reinsurance policies for mean-variance insurers. Insurance: Mathematics and Economics 49 (1):145–54.
   Web of Science ®Google Scholar
• Zhao, Q., Y. Shen, and J. Wei. 2014a. ConsumptionCinvestment strategies with non-exponential discounting and logarithmic utility. European Journal of Operational Research 238 (3):824–35.
   Web of Science ®Google Scholar
• Zhao, Q., R. Wang, and J. Wei. 2016. Exponential utility maximization for an insurer with time-inconsistent preferences. Insurance: Mathematics and Economics 70:89–104.
   Web of Science ®Google Scholar
• Zhao, Q., J. Wei, and R. Wang. 2014b. On dividend strategies with non-exponential discounting. Insurance: Mathematics and Economics 58:1–13.
   Web of Science ®Google Scholar
• Zhao, Y., P. Chen, and H. Yang. 2017. Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes. Insurance: Mathematics and Economics 74:135–46.
   Web of Science ®Google Scholar
• Zhao, Y., R. Wang, D. Yao, and P. Chen. 2015. Optimal dividends and capital injections in the dual model with a random time horizon. Journal of Optimization Theory and Applications 167 (1):272–95.
   Web of Science ®Google Scholar