The product of dependent random variables with applications to a discrete-time risk model

2016/06/12 by Jikun Chen, Hui Xu, Chen, Jikun +3 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.1606.03651

openalex publication_date 2016/06/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let X be a real valued random variable with an unbounded distribution F and let Y be a nonnegative valued random variable with a unbounded distribution G, which satisfy that P(Xgt;x|Y=y)∼ h(y)P(Xgt;x) holds uniformly for y≥0 as x→ ∞. Under the condition that G(bx)=o( H(x)) holds for all constant b>0, we proved that F\inL(γ) for some γ≥ 0 implied H∈ L(γ/β_G) and that F\inS(γ) for some γ≥ 0 implied H∈ S(γ/β_G), where H is the distribution of the product XY, and β_G is the right endpoint of G, that is, β_G=sup\y:~G(y)<1\∈ (0,∞], and when β_G=∞, γ/β_G is understood as 0. Furthermore, in a discrete-time risk model in which the net insurance loss and the stochastic discount factor are equipped with a dependence structure, a general asymptotic formula for the finite-time ruin probability is obtained when the net insurance loss has a subexponential tail.

Citations

• Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks

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• Multivariate subexponentiality and interplay of insurance and financial risks in a renwal risk model
• The Bivariate regular variation of randomly weighted sums revisited in the presence of interdependence

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