Dong Y, Wang D. Uniform asymptotics for ruin probabilities in a two-dimensional nonstandard renewal risk model with stochastic returns.
JOURNAL OF INEQUALITIES AND APPLICATIONS 2018;
2018:319. [PMID:
30839840 PMCID:
PMC6244751 DOI:
10.1186/s13660-018-1913-6]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/26/2018] [Accepted: 11/13/2018] [Indexed: 06/09/2023]
Abstract
In this paper, we consider a two-dimensional nonstandard renewal risk model with stochastic returns, in which the two lines of claim sizes form a sequence of independent and identically distributed random vectors following a bivariate Sarmanov distribution, and the two claim-number processes satisfy a certain dependence structure. When the two marginal distributions of the claim-size vector belong to the intersection of the dominated-variation class and the class of long-tailed distributions, we obtain uniform asymptotic formulas of finite-time and infinite-time ruin probabilities.
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