Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tai

By Qihe Tang, G. Tsitsiashvili. 2003

387 citations recorded by the source corpus.

This paper investigates the probability of ruin within finite horizon for a discrete time risk model, in which the reserve of an insurance business is currently invested in a risky asset. Under assumption that the risks are heavy tailed, some precise estimates for the finite time ruin probability are derived, which confirm a folklore that the ruin probability is mainly determined by whichever of insurance risk and financial risk is heavier than the other. In addition, some discussions on the heavy tails of the sum and product of independent random variables are involved, most of which have their own merits.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/993fd5a0028b9be96f4def401841c0b86eecb111

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Citations in the corpus

From light tails to heavy tails through multiplier (2008, background): “The study shows that risky investments may impair the insurer’s solvency just as severely as do large claims; see Norberg (1999), Kalashnikov and Norberg (2002), and Tang and Tsitsiashvili (2003).”
Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory (2003, background): “�). ( 17 ) 4 An application to ruin under dependent return rates”
Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model (2010, background): “It is commonly acknowledged that risky investments may impair the insurer’s solvency just as severely as large claims do; see Kalashnikov and Norberg (2002) and Tang and Tsitsiashvili (2003).”
Approximation of the tail probability of randomly weighted sums and applications (2009, background): “Tang and Tsitsiashvili [25] established the asymptotic formulation regarding the maxima Mn as in (1.2) for the case when {X i , i ≥ 1} belong to the intersection of the longtailed class and dominant variation class, and {Θi , i ≥ 1} are structured through the independent sequence {Yi , i ≥ 1} of r.v”
Randomly weighted sums of subexponential random variables with application to capital allocation (2014, background): “5.1 Proof of Theorem 1 Following the proof of Proposition 5.1 of Tang and Tsitsiashvili (2003b) with some obvious changes, we obtain Lemma 1 Let X1, . . . , Xn be n real-valued independent random variables, each distributed by Fi satisfying Fi ∈ L and Fi(x) F(x) for some F ∈ S and all i = 1, . . .…”
Integrated insurance risk models with exponential Lévy investment (2008, methodology): “More general models with exponential Lévy investment are considered in Paulsen [22], see also Tang and Tsitsiashvili [25].”
Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory (2005, neutral): “[2]: Lemma 2.”
Precise large deviations for sums of random variables with consistently varying tails (2004, background): “This is a part of Lemma 3.5 of Tang and Tsitsiashvili (2003).”
The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables (2010, background): “Furthermore, by Lemma 3.5 of Tang and Tsitsiashvili (2003), there is some constant p > 0 such that x−p = o(Ḡ(x)).”
Insensitivity to Negative Dependence of the Asymptotic Behavior of Precise Large Deviations (2006, methodology): “The following lemma is a combination of Proposition 2.2.1 of Bingham et al. (1987) and Lemma 3.5 of Tang and Tsitsiashvili (2003): Lemma 2.1.”
Asymptotics of random contractions (2010, methodology): “…properties of random contractions are Kotz and Nadarajah (2000), Galambos and Simonelli (2004), Gomes et al. (2004), Maulik and Resnick (2004), Tang and Tsitsiashvili (2003, 2004), Jessen and Mikosch (2006), D’Auria and Resnick (2006, 2008), Tang (2006, 2008), Denisov and Zwart (2007), Pakes…”