Erlangian Approximations for Finite-Horizon Ruin Probabilities

Asmussen, Søren; Avram, Florin; Usabel, Miguel

doi:10.2143/ast.32.2.1029

Cited by 113 publications

(103 citation statements)

References 16 publications

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“…The uniformity of relation (3.1) also makes it possible to change the horizon t into a nonnegative random variable as long as it is independent of the risk system, as done recently by Asmussen et al [2] and Avram and Usabel [5] . In fact, we have the following consequence of Theorem 3.1: Corollary 3.2.…”

Section: ð3:7þmentioning

confidence: 99%

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Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation

Tang

2004

Stochastic Models

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This paper investigates the finite time ruin probability in the renewal risk model. Under some mild assumptions on the tail probabilities of the claim size and of the inter-occurrence time, a simple asymptotic relation is established as the initial surplus increases. In particular, this asymptotic relation is requested to hold uniformly for the horizon varying in a relevant infinite interval. The uniformity allows us to consider that the horizon flexibly varies as a function of the initial surplus, or to change the horizon into any nonnegative random variable as long as it is independent of the risk system.

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Section: ð3:7þmentioning

confidence: 99%

“…1, and to Asmussen et al [2] and Avram and Usabel [5] , who considered, with some inspiring probabilistic explanations, the finite time ruin probability associated with the deficit at ruin with a random horizon T which has a general phase-type distribution and is independent of the risk systems.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation

Tang

2004

Stochastic Models

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“…As regards the rate of convergence, the form of the PDF of Γ n,n/t implies that, in the case that f is C 2 at t, the decay of the error E[f (Γ n,n/t )] − f (t) is linear in 1/n, in line with [2,Theorem 6], and that, moreover, E[f (Γ n,n/t )] admits the following expansion if the function f is C 2k at t:…”

Section: Introductionmentioning

confidence: 74%

Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications

Mijatović

Pistorius

Stolte

2015

Journal of Applied Probability

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Abstract. We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Lévy bridge process that relies in part on a randomisation of the time parameter. We establish this recursion for general Lévy processes and derive its explicit form for mixed-exponential jump-diffusions, a dense subclass (in the sense of weak approximation) of Lévy processes, which includes Brownian motion with drift, Kou's double-exponential model and hyper-exponential jump-diffusion models. We present a highly accurate numerical realisation and derive error estimates. By way of illustration the method is applied to the valuation of range accruals and barrier options under exponential Lévy models and Bates-type stochastic volatility models with exponential jumps. Compared with standard Monte Carlo methods, we find that the method is significantly more efficient.

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“…Some of the first are illustrated in this paper; the latter may be seen in the companion paper of Asmussen et al (2002), where a numerical method for computing finite time ruin probabilities without Laplace inversion is proposed and implemented.…”

Section: "Phase-type" Modelingmentioning

confidence: 99%