Abstract
Recently, Chen (2011) studied the finite-time ruin probability in a discrete-time risk model in which the insurance and financial risks form a sequence of independent and identically distributed random pairs with common bivariate Farlie-Gumbel-Morgenstern (FGM)distribution. The parameter θ of the FGMdistribution governs the strength of dependence, with a smaller value of θ corresponding to a less risky situation. For the subexponential case with -1. <. θ. ≤. 1, a general asymptotic formula for the finite-time ruin probability was derived. However, the derivation there is not valid for the least risky case θ. =. -. 1. In this paper, we complete the study by extending it to θ. =. -. 1. The new formulas for θ. =. -. 1 look very different from, but are intrinsically consistent with, the existing one for -1. <. θ. ≤. 1, and they offer a quantitative understanding on how significantly the asymptotic ruin probability decreases when θ switches from its normal range to its negative extremum.
| Original language | English |
|---|---|
| Pages (from-to) | 98-106 |
| Number of pages | 9 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 62 |
| DOIs | |
| Publication status | Published - 1 May 2015 |
| Externally published | Yes |
Keywords
- Asymptotics
- Farlie-Gumbel-Morgenstern distribution
- Finite-time ruin probability
- Primary
- Product of dependent random variables
- Secondary
- Subexponential distribution