Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments

By Qihe Tang, G. Tsitsiashvili. Advances in Applied Probability, 2004

160 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/2d9705ad47d0eb118544f3a73053d6cc02b951e8

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Citations in the corpus

Tail Probabilities of Randomly Weighted Sums of Random Variables with Dominated Variation (2006, background): “3) have been extensively investigated by Nyrhinen[6,7] and Tang and Tsitsiashvili[9,11], among others.”
Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims (2009, background): “The proof of Lemma 3.2, below, parallels the argument in Tang and Tsitsiashvili (2004) with some adjustments.”
Ruin Models with Investment Income (2008, methodology): “In [74] a discrete time version of (2.4) is given, while [16, 43, 44, 64, 65 ] all focus on the asymptotics of ruin probabilities, to be briefly reviewed below.”
From light tails to heavy tails through multiplier (2008, background): “(3.9) Since F ∈ R−∞, by Lemma A.3 of Tang and Tsitsiashvili (2004) we have ∫ ∞ M0 F ( x y ) G(dy) ∼ H(x).”
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”
Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory (2005, unknown): “[3] for the definition of F ∈ ERV (−α,−β)) and certain moment condition on {Yi}∞i=1, Tang and Tsitsiashvili proved that ψ(x, n) ∼ n ∑”
Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model (2010, unknown): “Hence, following the same lines of the proof of Theorem 3.1 of Tang and Tsitsiashvili (2004) with some obvious modifications (see also Section 4 of Chen and Ng (2007)), we obtain lim n→∞ lim supx→∞ 1 F̄ (x) Pr ( ∞∑ k=n+1 Xke −rτk > x ) = lim n→∞ lim supx→∞ ∞∑ k=n+1 Pr(Xke−rτk > x) F̄ (x) = 0.”
Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model (2007, unknown): “Using Theorem 3.1 of Tang and Tsitsiashvili (2004), we find that Pr(Dδ(∞) > x) ∼ ∞∑ k=1 Pr(Xke −δτk > x) = ∫ ∞ 0− F(xeδs) dλs.”
The Tail Probability of Discounted Sums of Pareto-like Losses in Insurance (2005, background): “EXAMPLE 1.1. Just as in Nyrhinen [2] and Tang & Tsitsiashvili [3, 4 ], consider a discrete time risk model, in which the surplus of the insurance company is invested into a risky asset that generates a random, possibly negative, return rate in each year.”
Asymptotics of random contractions (2010, background): “2 Proof of Theorem 3.1 a) The claim in (3.4) follows by Lemma A.5 of Tang and Tsitsiashvili (2004) and Theorem 3 of Hashorva (2009).”