Asymptotics for a discrete-time risk model with Gamma-like insurance risks. Issue 6 (2nd July 2016)

• Record Type: Journal Article
• Authors: Yang, Yang; Yuen, Kam C.
• Is Part Of: Scandinavian actuarial journal. Volume 2016:Issue 6(2016)
• Page Start: 565
• Page End: 579
• Publication Date: 2016-07-02
• Subjects: asymptotics -- Gamma-like tail -- insurance and financial risks -- finite-time and infinite-time ruin probabilities -- stochastic discounted value of aggregate net losses -- Sarmanov distribution; 62P05 -- 62E10 -- 91B30; Insurance, Life -- Mathematics -- Periodicals; Insurance -- Mathematics -- Periodicals; 368.01
• DOI: 10.1080/03461238.2015.1004802
• Languages: English
• ISSNs: 0346-1238

Abstract

Abstract : Consider a discrete-time insurance risk model with insurance and financial risks. Within period, the net insurance loss is denoted by and the stochastic discount factor over the same time period is denoted by . Assume that form a sequence of independent and identically distributed real-valued random variables with common distribution ; are another sequence of independent and identically distributed positive random variables with common distribution ; and the two sequences are mutually independent. Under the assumptions that is Gamma-like tailed and has a finite upper endpoint, we derive some precise formulas for the tail probability of the present value of aggregate net losses and the finite-time and infinite-time ruin probabilities. As an extension, a dependent risk model is considered, where each random pair of the net loss and the discount factor follows a bivariate Sarmanov distribution.