The Expected Discounted Penalty Function with Random Income under Stochastic Discount Interest Force

Abstract:

We study the delayed risk model with random premium income. The premium process is not a linear function of time in contrast with the classical model, but a Poisson process which is also independent of the claim process. We shall consider the case where the discount interest process is no longer a constant in comparison with the classical expected discounted penalty function, but a stochastic interest driven by Poisson process and Wiener process. The expected discounted penalty function in the delayed renewal model is expressed in terms of the corresponding Gerber-Shiu function in the ordinary renewal model. The obtained results can be viewed as the discrete analogy of the classical Sparre-Anderson risk model.

• Periodical: Advanced Materials Research (Volumes 113-116)
• Pages: 378-381
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.113-116.378
• Online since: June 2010
• Authors: Wen Guang Yu, Zhi Liu
• Keywords: Delayed Renewal Risk Process, Expected Discounted Penalty Function, Ruin Probability, Sparre Anderson Model, Stochastic Interest Process

References

[1] Z. Bao, Z. Ye, The Gerber-Shiu discounted penalty function in the delayed renewal risk process with random income. Applied Mathematics and Computation, Vol. 184(2007), pp.559-566.

DOI: 10.1016/j.amc.2006.06.076

[2] K.P. Pavlova, G.E. Willmot, The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function. Insurance: Mathematics and Economics, Vol. 35(2004), pp.267-277.

DOI: 10.1016/j.insmatheco.2004.04.006

[3] X. Zhao, J. Liu, A class of ruin problem in classical risk process under stochastic interest. Applied Mathematics: A Journal of Chinese Universities, Vol. 20A(2005), pp.313-319.

[4] G.E. Willmot, A note on a class of delayed renewal risk processes. Insurance: Mathematics and Economics, Vol. 34(2004) pp.251-257.

DOI: 10.1016/j.insmatheco.2003.12.005

[5] G.E. Willmot, D.C.M. Dickson, The Gerber-Shiu discounted penalty function in the stationary renewal risk model. Insurance: Mathematics and Economics, Vol. 32(2003), pp.403-411.

DOI: 10.1016/s0167-6687(03)00129-x

[6] G.E. Willmot, X.D. Lin, Lundburg Approximations for Compound Poisson Distributions with Insurance Applications, (Springer-Verlag, New York, 2001).

[7] S.M. Li, J. Garrido, On a general class of renewal risk process: analysis of the Gerber-Shiu Function. Advanceds in applied probability, Vol. 37(2005), pp.836-856.

DOI: 10.1239/aap/1127483750

[8] D.C.M. Dickson, C. Hipp, On the time to ruin for Erlang (2) risk processes. Insurance: Mathematics and Economics, Vol. 29(2001), pp.333-344.

DOI: 10.1016/s0167-6687(01)00091-9

[9] G.E. Willmot, D.C.M. Dickson, The Gerber-Shiu discounted penalty function in the stationary renewal risk model. Insurance: Mathematics and Economics, Vol. 32(2003), pp.403-411.

DOI: 10.1016/s0167-6687(03)00129-x