Luo, Kui; Wang, Guangming; Hu, Yijun Cox risk model with correlated classes of business. (English) Zbl 1212.91042 Wuhan Univ. J. Nat. Sci. 14, No. 5, 378-382 (2009). Summary: A correlated aggregate claim model with \(m\) dependent classes of insurance business is constructed, in which claim occurrences of \(m\) classes relate to Cox process and these claim processes are correlated. This Cox risk model with correlated classes of business is first transformed to the Cox model of \(n\) independent risk processes. Then, the generalized Lundberg exponent and Lundberg inequality are obtained by the martingale approach. Finally, an explicit expression of the Lundberg exponent is derived under a special condition. MSC: 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics 60G46 Martingales and classical analysis Keywords:Cox process; Lundberg inequality; ruin probability; martingale PDFBibTeX XMLCite \textit{K. Luo} et al., Wuhan Univ. J. Nat. Sci. 14, No. 5, 378--382 (2009; Zbl 1212.91042) Full Text: DOI References: [1] Grandell J. Aspects of Risk Theory [M]. New York: Springer-Verlag, 1991. · Zbl 0717.62100 [2] Ambagaspitiya R S. On the Distribution of a Sum of Correlated Aggregate Claims[J]. Insurance: Mathematics and Economics, 1998, 23(1): 15–19. · Zbl 0916.62072 [3] Wu Xueyuan, Yuen K C. A Discrete-Time Risk Model with Interaction between Classes of Business [J]. Insurance: Mathematics and Economics, 2003, 33(1): 117–133. · Zbl 1074.91031 [4] Yuen K C, Guo Junyi, Wu Xueyuan. On a Correlated Aggregate Claims Model with Poisson and Erlang Risk Process [J]. Insurance: Mathematics and Economics, 2002, 31(2): 205–214. · Zbl 1074.91566 [5] Wang G, Yuen K C. On a Correlated Aggregate Claims Model with Thinning-Structure [J]. Insurance: Mathematics and Economics, 2005, 36(3): 456–468. · Zbl 1120.62095 [6] Cossette H, Marceau E. The Discrete-Time Model with Correlated Classes of Business [J]. Insurance: Mathematics and Economics, 2000, 26(2–3): 133–149. · Zbl 1103.91358 [7] Grandell J. Doubly Stochastic Poisson Processes [M]. Berlin: Springer-Verlag, 1976. · Zbl 0339.60053 [8] Cai Jun, Dickson David C M. Ruin Probabilities with a Markov Chain Interest Model [J]. Insurance: Mathematics and Economics, 2004, 35(3): 513–525. · Zbl 1122.91340 [9] Lu Yi, Li Shuanming. On the Probability of Ruin in a Markov-Modulated Risk Model [J]. Insurance: Mathematics and Economics, 2005, 37(3): 522–532. · Zbl 1129.60066 [10] Albrecher H, Onno J B. On the Discounted Penalty Function in a Markov-Dependent Risk Model [J]. Insurance: Mathematics and Economics, 2005, 37(3): 650–672. · Zbl 1129.91023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.