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Advances in Mathematical Physics
Volume 2016, Article ID 1967872, 13 pages
http://dx.doi.org/10.1155/2016/1967872
Research Article

Explicit Solution of Reinsurance-Investment Problem for an Insurer with Dynamic Income under Vasicek Model

Faculty of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China

Received 14 October 2015; Accepted 22 December 2015

Academic Editor: Doojin Ryu

Copyright © 2016 De-Lei Sheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Y. Cao and J. Xu, “Proportional and excess-of-loss reinsurance under investment gains,” Applied Mathematics and Computation, vol. 217, no. 6, pp. 2546–2550, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. Y. Cao and X. Zeng, “Optimal proportional reinsurance and investment with minimum probability of ruin,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5433–5438, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. M. Grasselli, “A stability result for the HARA class with stochastic interest rates,” Insurance: Mathematics and Economics, vol. 33, no. 3, pp. 611–627, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. J. Li and R. Wu, “Optimal investment problem with stochastic interest rate and stochastic volatility: maximizing a power utility,” Applied Stochastic Models in Business and Industry, vol. 25, no. 3, pp. 407–420, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. T. Pang, “Stochastic portfolio optimization with log utility,” International Journal of Theoretical and Applied Finance, vol. 9, no. 6, pp. 869–887, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. C. Munk and A. Rubtsov, “Portfolio management with stochastic interest rates and inflation ambiguity,” Annals of Finance, vol. 10, no. 3, pp. 419–455, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. R. Korn and H. Kraft, “A stochastic control approach to portfolio problems with stochastic interest rates,” SIAM Journal on Control and Optimization, vol. 40, no. 4, pp. 1250–1269, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. D. Hainaut, “Dynamic asset allocation under VaR constraint with stochastic interest rates,” Annals of Operations Research, vol. 172, no. 1, pp. 97–117, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. O. Vasicek, “An equilibrium characterization of the term structure,” Journal of Financial Economics, vol. 5, no. 2, pp. 177–188, 1977. View at Publisher · View at Google Scholar
  10. R. C. Merton, “Optimum consumption and portfolio rules in a continuous-time model,” Journal of Economic Theory, vol. 3, no. 4, pp. 373–413, 1971. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. H. U. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, Berlin, Germany, 1993.
  12. G. Guan and Z. Liang, “Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework,” Insurance: Mathematics and Economics, vol. 57, pp. 58–66, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. G. Guan and Z. Liang, “Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks,” Insurance: Mathematics & Economics, vol. 55, pp. 105–115, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. A. Gu, X. Guo, Z. Li, and Y. Zeng, “Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model,” Insurance: Mathematics and Economics, vol. 51, no. 3, pp. 674–684, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus