Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims

Albrecher, Hansjörg; Vatamidou, Eleni

doi:10.3390/risks7040104

Cited by 2 publications

(1 citation statement)

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“…The effect of such an approximation on the resulting ruin probability is discussed by Vatamidou et al (2013Vatamidou et al ( , 2014 on the basis of the Pollaczek-Khintchine formula. A similar approach is also feasible in the Sparre-Andersen model; see Albrecher and Vatamidou (2019). In the last references the approximation is used for theoretical distribution functions, but certainly one can approximate empirical distribution functions based on a sample by means of the EM-algorithm; see Asmussen et al (1996).…”

Section: Introductionmentioning

confidence: 99%

On Computations in Renewal Risk Models—Analytical and Statistical Aspects

Strini

Thonhauser

2020

Risks

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We discuss aspects of numerical methods for the computation of Gerber-Shiu or discounted penalty-functions in renewal risk models. We take an analytical point of view and link this function to a partial-integro-differential equation and propose a numerical method for its solution. We show weak convergence of an approximating sequence of piecewise-deterministic Markov processes (PDMPs) for deriving the convergence of the procedures. We will use estimated PDMP characteristics in a subsequent step from simulated sample data and study its effect on the numerically computed Gerber-Shiu functions. It can be seen that the main source of instability stems from the hazard rate estimator. Interestingly, results obtained using MC methods are hardly affected by estimation.

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Section: Introductionmentioning

confidence: 99%

On Computations in Renewal Risk Models—Analytical and Statistical Aspects

Strini

Thonhauser

2020

Risks

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Martingale Approach to Derive Lundberg-Type Inequalities

2020

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In this paper, we find the upper bound for the tail probability Psupn⩾0∑i=1nξi>x with random summands ξ1,ξ2,… having light-tailed distributions. We find conditions under which the tail probability of supremum of sums can be estimated by quantity ϱ1exp{−ϱ2x} with some positive constants ϱ1 and ϱ2. For the proof we use the martingale approach together with the fundamental Wald’s identity. As the application we derive a few Lundberg-type inequalities for the ultimate ruin probability of the inhomogeneous renewal risk model.

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Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims

Cited by 2 publications

References 29 publications

On Computations in Renewal Risk Models—Analytical and Statistical Aspects

On Computations in Renewal Risk Models—Analytical and Statistical Aspects

Martingale Approach to Derive Lundberg-Type Inequalities

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