Skip to main content
SpringerLink
Log in

Optimal time-consistent investment and reinsurance strategy for mean-variance insurers under the inside information

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, we consider the problem of the optimal time-consistent investment and proportional reinsurance strategy under the mean-variance criterion, in which the insurer has some inside information at her disposal concerning the future realizations of her claims process. It is assumed that the surplus of the insurer is governed by a Brownian motion with drift, and the insurer has the possibility to reduce the risk by purchasing proportional reinsurance and investing in financial markets. We first formulate the problem and provide a verification theorem on the extended Hamilton-Jacobi-Bellman equations. Then, the closed-form expression is obtained for the optimal strategy of the optimization problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bai, L., Guo,J. Optimal proportional reinsurance and investment with multiple risky assets and no short constraint. Insurance: Mathematics and Economics, 42(3): 968–975 (2008).

    MathSciNet  MATH  Google Scholar 

  2. Bai, L., Zhang, H. Dynamic mean-variance problem with constrained risk control for the insurers. Mathematical Methods of Operations Research, 68(1): 181–205 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  3. Baltas, I.D., Frangos, N.E., Yannacopoulos A.N. Optimal investment and reinsurance policies in insurance markets under the effect of inside information. Applied Stochastic Models in Business and Industry, 28(6): 506–528 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  4. Bäuerle, N. Benchmark and mean-variance problems for insurers. Mathematical Methods of Operations Research, 62(1): 159–165 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  5. Biagini, F., Øksendal, B. A general stochastic calculus approach to insider trading. Applied Mathematics & Optimization, 52(2): 167–181 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  6. Cao, Y., Wan, N. Optimal proportioanal reinsurance and investment based on Hamilton-Jacobi-Bellman equation. Insurance: Mathematics and Economics, 45(2): 157–162 (2009).

    MathSciNet  MATH  Google Scholar 

  7. Delong, L., Gerrard, R. Mean-variance portfolio selection for a nonlife insurance company. Mathematical Methods of Operations Research, 66(2): 339–367 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  8. Di Nunno, G., Øksendal, B., Proske, F. Malliavin Calculus for Lévy Processes with Applications to Finance. Springer-Verlag, Berlin, 2009.

    Book  Google Scholar 

  9. Hata, H., Kohatsu-Higa, A. A market model with Medium/Long term effects due to an insider. Quantitative Finance, 13(3): 1–17 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  10. Hipp, C., Plum, M. Optimal investment for insurers. Insurance: Mathematics and Economics, 27(2): 215–228 (2000).

    MathSciNet  MATH  Google Scholar 

  11. Ito, K. Extension of stochastic integrals. Proceedings of the International Symposium on Stochastic Differential Equations, Kyoto, 1976, 95–109.

    Google Scholar 

  12. Kaluszka, M. An extension of Arrows result on optimality of a stop-loss contract. Insurance: Mathematics and Economics, 35(3): 527–536 (2004).

    MathSciNet  MATH  Google Scholar 

  13. Liang, Z., Chuen Yuen, K., Guo, J. Optimal Proportional reinsurance and investment in a stock market with Ornstein–Uhlenbeck process. Insurance: Mathematics and Economics, 49(2): 207–215 (2011).

    MathSciNet  MATH  Google Scholar 

  14. Li, D., Ng, W.L. Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation. Mathematical Finance, 10(3): 387–406 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  15. Luo, S., Taksar, M., Tsoi, A. On reinsurance and investment for large insurance portfolios. Insurance: Mathematics and Economics, 42: 434–444 (2008).

    MathSciNet  MATH  Google Scholar 

  16. Markowitz, H.M. Portfolio selection. Jornal of Finance, 7(1): 77–91 (1952).

    Google Scholar 

  17. Peng, X., Hu, Y. Optimal proportional reinsurance and investment under partial information. Insurance: Mathematics and Economics, 53(2): 416–428 (2013).

    MathSciNet  MATH  Google Scholar 

  18. Pikovsky, I., Karatzas, I. Anticipative portfolio optimization. Advances in Applied Probability, 28(4): 1095–1122 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  19. Promislow, S.D., Young, V.R. Minimizing the probability of ruin when claims follow Brownian motion with drift. North American Actuarial Journal, 9 (3): 110–128 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  20. Protter, P. Stochastic Integration and Stochastic Differential Equations, 2nd ed. Springer-Verlag, Berlin, 2004.

    MATH  Google Scholar 

  21. Schimidli, H. On minimizing the ruin probability by investment and reinsurance. Annals of Applied Probability, 12(3): 890–907 (2002).

    Article  MathSciNet  Google Scholar 

  22. Zeng, Y., Li, Z. Optimal time-consistent investment and reinsurance policies for mean-variance insurers. Insurance: Mathematics and Economics, 49(1): 145–154 (2011).

    MathSciNet  MATH  Google Scholar 

  23. Zhou, X.Y., Li, D. Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework. Applied Mathematics and Optimization, 42(1): 19–33 (2000).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Jing Cao & Yi-jun Hu

  2. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, 430074, China

    Jing Cao

  3. School of Science, Wuhan University of Technology, Wuhan, 430070, China

    Xing-chun Peng

Authors
  1. Jing Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xing-chun Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yi-jun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by the Natural Science Foundation of Hubei Province under Grant 2015CKB737, and the National Natural Science Foundation of China under Grant No. 11371284.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, J., Peng, Xc. & Hu, Yj. Optimal time-consistent investment and reinsurance strategy for mean-variance insurers under the inside information. Acta Math. Appl. Sin. Engl. Ser. 32, 1087–1100 (2016). https://doi.org/10.1007/s10255-016-0629-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-016-0629-y

Keywords

2000 MR Subject Classification

Search

Navigation