کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5077511 | 1374134 | 2010 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An insurance risk model with stochastic volatility
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آمار و احتمال
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper, we extend the Cramér-Lundberg insurance risk model perturbed by diffusion to incorporate stochastic volatility and study the resulting Gerber-Shiu expected discounted penalty (EDP) function. Under the assumption that volatility is driven by an underlying Ornstein-Uhlenbeck (OU) process, we derive the integro-differential equation which the EDP function satisfies. Not surprisingly, no closed-form solution exists; however, assuming the driving OU process is fast mean-reverting, we apply the singular perturbation theory to obtain an asymptotic expansion of the solution. Two integro-differential equations for the first two terms in this expansion are obtained and explicitly solved. When the claim size distribution is of phase-type, the asymptotic results simplify even further and we succeed in estimating the error of the approximation. Hyper-exponential and mixed-Erlang distributed claims are considered in some detail.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Insurance: Mathematics and Economics - Volume 46, Issue 1, February 2010, Pages 52-66
Journal: Insurance: Mathematics and Economics - Volume 46, Issue 1, February 2010, Pages 52-66
نویسندگان
Yichun Chi, Sebastian Jaimungal, X. Sheldon Lin,