Cox risk model with variable premium rate and stochastic return on investment

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:256

Article

Xu, Lin¹  Yang, Hailiang²  Wang, Rongming^3,4 

[1] Anhui Normal Univ, Sch Math & Comp Sci, Wuhu, Anhui, Peoples R China

[2] Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Hong Kong, Peoples R China

[3] E China Normal Univ, Sch Finance & Stat, Shanghai 200241, Peoples R China

[4] E China Normal Univ, Res Ctr Int Finance & Risk Management, Shanghai 200241, Peoples R China

关键词: Cox risk model;    Optimal investment;    Expected discounted penalty function;    Variable premium rate;   

DOI  :  10.1016/j.cam.2013.07.016

来源: Elsevier

【 摘 要 】

This paper studies the ruin probability for a Cox risk model with intensity depending on premiums and stochastic investment returns, and the model proposed in this paper allows the dependence between premiums and claims. When the surplus is invested in the bond market with constant interest force, coupled integral equations for the Gerber Shiu expected discounted penalty function (GS function) are derived; together with the initial value and Laplace transformation of the GS function, we provide a numerical procedure for obtaining the GS function. When the surplus can be invested in risky asset driven by a drifted Brownian motion, we focus on finding a minimal upper bound of ruin probability and find that optimal piecewise constant policy yields the minimal upper bound. It turns out that the optimal piecewise constant policy is asymptotically optimal when initial surplus tends to infinity. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free