Share This Article:

Total Duration of Negative Surplus for a Diffusion Surplus Process with Stochastic Return on Investments

Abstract Full-Text HTML XML Download Download as PDF (Size:159KB) PP. 1674-1679
DOI: 10.4236/am.2012.311231    4,227 Downloads   5,750 Views  

ABSTRACT

In this paper, we consider a Brownian motion risk model with stochastic return on investments. Using the strong Markov property and exploiting the limitation idea, we derive the Laplace-Stieltjes Transform(LST) of the total duration of negative surplus. In addition, two examples are also present.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

H. You and C. Yin, "Total Duration of Negative Surplus for a Diffusion Surplus Process with Stochastic Return on Investments," Applied Mathematics, Vol. 3 No. 11, 2012, pp. 1674-1679. doi: 10.4236/am.2012.311231.

References

[1] J. Paulsen and H. K. Gjessing, “Optimal Choice of Dividend Barriers for a Risk Process with Stochastic Return on Investments,” Insurance: Mathematics and Economics, Vol. 20, No. 3, 1997, pp. 215-223. doi:10.1016/S0167-6687(97)00011-5
[2] J. Paulsen, “Risk Theory in a Stochastic Economic Environment,” Stochastic Processes and Their Applications, Vol. 46, No. 2, 1993, pp. 327-361. doi:10.1016/0304-4149(93)90010-2
[3] N. Ikeda and S. Watanabe, “Stochastic Differential Equations and Diffusion Processes,” North-Holland Publishing Company, Amsterdam, 1981.
[4] A. D. Egdio dos Reis, “How Long Is the Surplus below Zero?” Insurance: Mathematics and Economics, Vol. 12, No. 1, 1993, pp. 23-38. doi:10.1016/0167-6687(93)90996-3
[5] C. S. Zhang and R. Wu, “Total Duration of Negative Surplus for the Compound Poisson Process That Is Perturbed by Diffusion,” Insurance: Mathematics and Economics, Vol. 39, No. 3, 2002, pp. 517-532.
[6] S. N. Chiu and C. C. Yin, “On Occupation Times for a Risk Process with Reserve-Dependent Premium,” Stochastic Models, Vol. 18, No. 2, 2001, pp. 245-255. doi:10.1081/STM-120004466
[7] J. M. He, R. Wu and H. Y. Zhang, “Total Duration of Negative Surplus for the Risk Model with Debit Interest,” Statistics and Probability Letters, Vol. 79, No. 10, 2009, pp. 1320-1326. doi:10.1016/j.spl.2009.02.005
[8] W. Wang and J. M. He, “Total Duration of Negative Surplus for a Brownian Motion Risk Model with Interest,” Acta Mathematica Sinica, 2012, (Submitted).
[9] L. Breiman, “Probability,” Addison-Wesley, Reading, 1968.
[10] J. Cai, H. U. Gerber and H. L. Yang, “Optimal Dividends in an Ornstein-Uhlenbeck Type Model with Credit and Debit Interest,” North American Actuarial Journal, Vol. 10, No. 2, 2006, pp. 94-119.
[11] M. Abramowitz and I. A. Stegun, “Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables United States Department of Commerce,” US Government Printing Office, Washington DC, 1972.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.