Advanced Search
Article Contents
Article Contents

Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer

This work was supported by the National Natural Science Foundation for the Youth of China (Grants 11301081, 11401073), the Science Research Project of Educational Department of Liaoning Province of China (Grants. L2014188, L2015097 and L2014186), the Research Funding for Doctor Start-Up Program of Liaoning Province (Grant 201601245), the Fundamental Research Funds for Central Universities in China (Grant DUT15LK25), the Simons Foundation through Grant No. 357963 (Y.Z.), a start-up grant from the George Washington University (Y.Z.), Loyola Marymount University CSE continuing Faculty Research grant (Y.M.), and a start-up grant from Loyola Marymount University (Y.M.).

Abstract Full Text(HTML) Related Papers Cited by
  • We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions for the solutions of the regular-singular control problem. Finally we apply the maximum principles to solve the investment and dividend problem of an insurer.

    Mathematics Subject Classification: Primary: 93E20, 60H30; Secondary: 91B30.


    \begin{equation} \\ \end{equation}
  • 加载中
  •   D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge university press, New York, 2009. doi: 10.1017/CBO9780511809781.
      F. Avram , Z. Palmowski  and  M. R. Pistorius , On Gerber-Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function, Ann. Appl. Probab., 25 (2015) , 1868-1935.  doi: 10.1214/14-AAP1038.
      P. Azcue  and  N. Muler , Optimal investment policy and dividend payment strategy in an insurance company, Ann. Appl. Probab., 20 (2010) , 1253-1302.  doi: 10.1214/09-AAP643.
      F. Baghery  and  B. Oksendal , A maximum principle for stochastic control with partial information, Stoch. Anal. Appl., 25 (2007) , 705-717.  doi: 10.1080/07362990701283128.
      M. Belhaj , Optimal dividend payments when cash reserves follow a jump-diffusion process, Math. Finance, 20 (2010) , 313-325.  doi: 10.1111/j.1467-9965.2010.00399.x.
      S. Browne , Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin, Math. Oper. Res., 20 (1995) , 937-958.  doi: 10.1287/moor.20.4.937.
      G. Cheng , R. Wang  and  K. Fan , Optimal risk and dividend control of an insurance company with exponential premium principle and liquidation value, Stochastics, 88 (2016) , 904-926.  doi: 10.1080/17442508.2016.1163362.
      B. De Finetti , Su un'impostazione alternativa della teoria collettiva del rischio, Transactions of the XVth International Congress of Actuaries, 2 (1957) , 433-443. 
      R. J. Elliott  and  T. K. Siu , A stochastic differential game for optimal investment of an insurer with regime switching, Quant. Finance, 11 (2011) , 365-380.  doi: 10.1080/14697681003591704.
      W. Guo , Optimal portfolio choice for an insurer with loss aversion, Insurance Math. Econom., 58 (2014) , 217-222.  doi: 10.1016/j.insmatheco.2014.07.004.
      M. Hafayed , M. Ghebouli , S. Boukaf  and  Y. Shi , Partial information optimal control of mean-field forward-backward stochastic system driven by Teugels martingales with applications, Neurocomputing, 200 (2016) , 11-21.  doi: 10.1016/j.neucom.2016.03.002.
      B. Højgaard  and  M. Taksar , Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy, Quant. Finance, 4 (2004) , 315-327.  doi: 10.1088/1469-7688/4/3/007.
      Z. Jin , H. Yang  and  G. G. Yin , Numerical methods for optimal dividend payment and investment strategies of regime-switching jump diffusion models with capital injections, Automatica, 49 (2013) , 2317-2329.  doi: 10.1016/j.automatica.2013.04.043.
      Z. Jin  and  G. Yin , Numerical methods for optimal dividend payment and investment strategies of Markov-modulated jump diffusion models with regular and singular controls, J. Optim. Theory Appl., 159 (2013) , 246-271.  doi: 10.1007/s10957-012-0263-7.
      X. Lin , C. Zhang  and  T. K. Siu , Stochastic differential portfolio games for an insurer in a jump-diffusion risk process, Math. Methods Oper. Res., 75 (2012) , 83-100.  doi: 10.1007/s00186-011-0376-z.
      C. S. Liu  and  H. Yang , Optimal investment for an insurer to minimize its probability of ruin, N. Am. Actuar. J., 8 (2004) , 11-31.  doi: 10.1080/10920277.2004.10596134.
      J. Liu , K. F. C. Yiu  and  T. K. Siu , Optimal investment of an insurer with regime-switching and risk constraint, Scand. Actuar. J., 7 (2014) , 583-601.  doi: 10.1080/03461238.2012.750621.
      E. Marciniak  and  Z. Palmowski , On the optimal dividend problem for insurance risk models with surplus-dependent premiums, J. Optim. Theory Appl., 168 (2016) , 723-742.  doi: 10.1007/s10957-015-0755-3.
      B. Oksendal  and  A. Sulém , Singular stochastic control and optimal stopping with partial information of Itô-Lévy processes, SIAM J. Control Optim., 50 (2012) , 2254-2287.  doi: 10.1137/100793931.
      H. Markovitz , Portfolio selection*, J. Finance, 7 (1952) , 77-91. 
      R. C. Merton , Optimum consumption and portfolio rules in a continuous-time model, J. Econom. Theory, 3 (1971) , 373-413.  doi: 10.1016/0022-0531(71)90038-X.
      M. I. Taksar , Optimal risk and dividend distribution control models for an insurance company, Math. Methods Oper. Res., 51 (2000) , 1-42.  doi: 10.1007/s001860050001.
      Y. Wang , A. Song  and  E. Feng , A maximum principle via Malliavin calculus for combined stochastic control and impulse control of forward-backward systems, Asian J. Control, 17 (2015) , 1798-1809.  doi: 10.1002/asjc.1097.
      F. Zhang , Stochastic maximum principle for mixed regular-singular control problems of forward-backward systems, J. Syst. Sci. Complex., 26 (2013) , 886-901.  doi: 10.1007/s11424-013-0287-6.
  • 加载中

Article Metrics

HTML views(2149) PDF downloads(261) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint