194
Views
3
CrossRef citations to date
0
Altmetric
Feature Articles

Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process

&

References

  • Azcue, P., and M. Muler. 2009. Optimal Investment Strategy to Minimize the Ruin Probability of an Insurance Company under Borrowing Constraints. Insurance: Mathematics and Economics 44: 26–34.
  • Belkina, T., C. Hipp, S. Luo, and M. Taksar. 2014. Optimal Constrained Investment in the Cramer-Lundburg model. Scandinavian Actuarial Journal 5: 383–404.
  • Belkina, T. A., and M. V. Norshteyn. 2012. Structure of Optimal Investment Strategy in a Dynamic Model for Risks with Diffusion Disturbances. In Analysis and Modeling of Economic Processes: The Collection of Articles, edited by V. Z. Belenky, vol. 9, pp. 103–112. Moscow: CEMI RAS. Available at www.cemi.rssi.ru/publication/books.
  • Bellman, R. 2008. Stability Theory of Differential Equations. New York: Dover.
  • Dufresne, F., and H. U. Gerber. 1991. Risk Theory for the Compound Poisson Process That Is Perturbed by Diffusion. Insurance: Mathematics and Economics 10: 51–59.
  • Eisenberg, J. 2014. Asymptotic Optimal Investment under Interest Rate for a Class of Subexponential Distributions. Scandinavian Actuarial Journal 8: 671–689.
  • Frolova, A., Yu. Kabanov, and S. Pergamenshchikov. 2002. In the Insurance Business Risky Investments Are Dangerous. Finance and Stochastics 6: 227–235.
  • Gaier, J., and P. Grandits. 2002. Ruin Probabilities in the Presence of Regularly Varying Tails and Optimal Investment. Insurance: Mathematics and Economics 30: 211–217.
  • Gaier, J., and P. Grandits. 2004. Ruin Probabilities and Investment under Interest Force in the Presence of Regularly Varying Tails. Scandinavian Actuarial Journal 4: 256–278.
  • Gaier, J., P. Grandits, and W. Schachermayer. 2003. Asymptotic Ruin Probabilities and Optimal Investment. Annals of Applied Probability 13: 1054–1076.
  • Gerber, H. U., and H. Yang. 2007. Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment. North American Actuarial Journal 11: 159–169.
  • Grandits, P. 2005. Minimal Ruin Probabilities and Investment under Interest Force for a Class of Subexponential Distributions. Scandinavian Actuarial Journal 6: 401–416.
  • Hipp, C., and M. Plum. 2000. Optimal Investment for Insurers. Insurance: Mathematics and Economics 27: 215–228.
  • Hipp, C., and M. Plum. 2003. Optimal Investment for Investors with State Dependent Income, and for Insurers. Finance and Stochastics 7: 299–321.
  • Hipp, C., and H. Schmidli. 2004. Asymptotics of Ruin Probabilities for Controlled Risk Processes in the Small Claims Case. Scandinavian Actuarial Journal 5: 321–335.
  • Konyukhova, N. B. 1983. Singular Cauchy Problems for Systems of Ordinary Differential Equations. U.S.S.R. Computational Mathematics and Mathematical Physics 23: 72–82.
  • Laubis, L., and J. E. Lin. 2008. Optimal Investment Allocation in a Jump Diffusion Risk Model with Investment: A Numerical Analysis of Several Examples. In Proceedings (electronic) of 43rd Actuarial Research Conference. https://www.soa.org/news-and-publications/publications/proceedings/arch/arch-2009-iss1.aspx.
  • Lin, X. 2009. Ruin Theory for Classical Risk Process That Is Perturbed by Diffusion with Risky Investments. Applied Stochastic Models in Business and Industry 25: 33–44.
  • Luo, S. 2008. Ruin Minimization for Insurers with Borrowing Constraints. North American Actuarial Journal 12: 143–174.
  • Luo, S., and M. Taksar. 2011. On Absolute Ruin Minimization under a Diffusion Approximation Model. Insurance: Mathematics and Economics 48: 123–133.
  • Lyapunov, A. M. 1992. The General Problem of the Stability of Motion. International Journal of Control 55: 531–534.
  • Paulsen, J., and H. K. Gjessing. 1997. Ruin Theory with Stochastic Return on Investments. Advances in Applied Probability 29: 965–985.
  • Schmidli, H. 2001. Optimal Proportional Reinsurance Policies in a Dynamic Setting. Scandinavian Actuarial Journal 1: 55–68.
  • Schmidli, H. 2002. On Minimizing the Ruin Probability by Investment and Reinsurance. Annals of Applied Probability 12: 890–907.
  • Schmidli, H. 2005. On Optimal Investment and Subexponential Claims. Insurance: Mathematics and Economics 36: 25–35.
  • Schmidli, H. 2008. Stochastic Control in Insurance. London: Springer.
  • Segerdahl, C. O. 1942. Über Einige Risikotheoretische Fragestellungen. Scandinavian Actuarial Journal 25: 43–83.
  • Taksar, M., and C. Markussen. 2003. Optimal Dynamic Reinsurance Policies for Large Insurance Portfolios. Finance and Stochastics 7: 97–121.
  • Teschl, G. 2012. Ordinary Differential Equations and Dynamical Systems. Providence, RI: American Mathematical Society.
  • Wasow, W. 1987. Asymptotic Expansions for Ordinary Differential Equations. New York: Dover.
  • Yang, H., and L. Zhang. 2005. Optimal Investment for Insurer with Jump-Diffusion Risk Process. Insurance: Mathematics and Economics 37: 615–634.

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:

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:

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.