Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model

Chadjiconstantinidis, Stathis; Politis, Konstadinos

doi:10.1016/j.insmatheco.2006.09.001

Cited by 13 publications

(7 citation statements)

References 16 publications

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“…Note that, similar ideas to those used here have also appeared in deriving the bounds regarding specific ruin-related quantities. For the exponential bounds, Chadjiconstantinidis and Politis (2007) and generalize similar results obtained by Garrido (1998, 1999), Willmot (2002), and . Psarrakos and Politis (2008) have also derived improved tail bounds for the joint distribution of the surplus prior to and at ruin in the classical risk model.…”

Section: Introductionsupporting

confidence: 82%

Refinements of two-sided bounds for renewal equations

Woo

2011

Insurance: Mathematics and Economics

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Section: Introductionsupporting

confidence: 82%

Refinements of two-sided bounds for renewal equations

Woo

2011

Insurance: Mathematics and Economics

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“…Remarks. (i) Putting x = 0 in (10) we obtain the following bound, derived originally by Chadjiconstantinidis and Politis (2007),…”

Section: Bounds For H(u X Y) When U > Xmentioning

confidence: 99%

Tail bounds for the joint distribution of the surplus prior to and at ruin

Psarrakos

Politis

2008

Insurance: Mathematics and Economics

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Keywords: Ruin probability, Time of ruin, Surplus process, Deficit at ruin, Defective renewal equation.We consider the classical risk model where claims Y 1 , Y 2 , . . . arrive in a compound Poisson process with rate λ. The claims are independent identically distributed non-negative random variables and have common distribution function P with finite mean µ. In the case where P has a density, we denote this density by p. We further assume that the claims are independent of the claimarrivals process. Premiums are paid to the insurer continuously at a rate c per unit time. The surplus of the insurer at time t is then U (t) = u + ct − Nt k=1 Y i , where u is the initial surplus and N t is the number of claims until t. We assume throughout that c > λµ, so that ruin is not certain to occur. Moreover, we write c = (1+θ)λµ, where θ is the relative security loading. Let T denote the time of ruin, i.e. the time that the surplus becomes negative for the first time and note that T is a defective random variable. The probability of ruin is then defined by ψ(u) = P (T < ∞|U (0) = u).(1)

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“…Next we verify that bound (12) is always tighter than bound (11). By Proposition 2.2 of Chadjiconstantinidis and Politis (2007) and (12), we have…”

Section: General Boundsmentioning

confidence: 91%

“…Recently, Willmot (2002) and Chadjiconstantinidis and Politis (2007) function. In Section 3, we construct also lower and upper bounds for H (u, y).…”

Section: Introductionmentioning

confidence: 99%

Tail bounds for the distribution of the deficit in the renewal risk model

Psarrakos

2008

Insurance: Mathematics and Economics

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Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model

Cited by 13 publications

References 16 publications

Refinements of two-sided bounds for renewal equations

Refinements of two-sided bounds for renewal equations

Tail bounds for the joint distribution of the surplus prior to and at ruin

Tail bounds for the distribution of the deficit in the renewal risk model

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