𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Gerber–Shiu discounted penalty functions for a risk model with two classes of claims

✍ Scribed by Zhimin Zhang; Shuanming Li; Hu Yang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
984 KB
Volume
230
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we consider the ruin problems for a risk model involving two independent classes of insurance risks. We assume that the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. When the generalized Lundberg equation has distinct roots with positive real parts, both of the Gerber-Shiu discounted penalty functions with zero initial surplus and the Laplace transforms of the Gerber-Shiu discounted penalty functions are obtained. Finally, some explicit expressions for the Gerber-Shiu discounted penalty functions with positive initial surplus are given when the claim size distributions belong to the rational family.

📜 SIMILAR VOLUMES

The Gerber–Shiu penalty functions for tw
The Gerber–Shiu penalty functions for two classes of renewal risk processes
✍ Lanpeng Ji; Chunsheng Zhang 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 967 KB

In this paper, we study the Gerber-Shiu functions for a risk model with two independent classes of risks. We suppose that both of the two claim number processes are renewal processes with phase-type inter-claim times. By re-composing and analyzing the Markov chains associated with two given phase-ty

On the expected discounted penalty funct
On the expected discounted penalty functions for two classes of risk processes under a threshold dividend strategy
✍ Zhaoyang Lu; Wei Xu; Decai Sun; Weiguo Han 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 710 KB

In this paper, the discounted penalty (Gerber-Shiu) functions for a risk model involving two independent classes of insurance risks under a threshold dividend strategy are developed. We also assume that the two claim number processes are independent Poisson and generalized Erlang (2) processes, resp

Asymptotics for the ruin probabilities o
Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims
✍ Yiqing Chen; Kam C. Yuen; Kai W. Ng 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 147 KB 👁 2 views

In this paper, we consider two dependent classes of insurance business with heavy-tailed claims. The dependence comes from the assumption that claim arrivals of the two classes are governed by a common renewal counting process. We study two types of ruin in the two-dimensional framework. For each ty