Non-exponential bounds for stop-loss premiums and ruin probabilities

Chadjiconstantinidis, Stathis; Politis, Konstadinos

doi:10.1080/03461230510009817

Cited by 14 publications

(10 citation statements)

References 6 publications

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“…This has been obtained by Chadjiconstantinidis and Politis (2005) and improves a similar result for the classical risk model by Cai and Garrido (1998). Our next result generalizes this upper bound by giving the corresponding bound for the severity of ruin.…”

Section: General Upper Boundssupporting

confidence: 55%

“…Note that a general lower bound for ψ(x) which is a refinement of (14), has been given recently by Chadjiconstantinidis and Politis (2005); various other, both upper and lower, bounds for ψ(x), are given in that paper.…”

Section: General Lower Boundsmentioning

confidence: 97%

“…Chadjiconstantinidis and Politis (2005), with the help of a lower bound that they proved for the stop-loss transform in the renewal risk model, have given the following bound for x ≥ 0:…”

Section: General Upper Boundsmentioning

confidence: 99%

See 2 more Smart Citations

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

Chadjiconstantinidis¹,

Politis²

2007

Insurance: Mathematics and Economics

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Section: General Upper Boundssupporting

confidence: 55%

Section: General Lower Boundsmentioning

confidence: 97%

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

Chadjiconstantinidis¹,

Politis²

2007

Insurance: Mathematics and Economics

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“…In the next section, we compare the performance of these bounds against other bounds that have been given recently for ψ(u), notably those by Garrido (1998, 1999), Politis (2005), Chadjiconstantinidis and Politis (2005).…”

Section: Upper and Lower Bounds For Ruin Probabilitiesmentioning

confidence: 96%

“…while upper bounds for ψ(u) can be found in Willmot and Lin (1997), Garrido (1998, 1999), Chadjiconstantinidis and Politis (2005). Next, we turn to consider lower bounds for H (u, x, y).…”

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

confidence: 97%

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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General bounds for the deficit distribution at ruin in the Sparre Andersen model

Gajek,

Rudź

2024

Lith Math J

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We present constructive methods that give upper and lower bounds of Ψ, the insurer’s deficit distribution at ruin time in the Sparre Andersen model. The methodology effectively provides monotone sequences of upper and lower bounds of Ψ, and those sequences converge to Ψ with exponential rate. Several new lower and upper bounds of Ψ are given. As an example, we introduce new bounds of the deficit distribution at ruin when the claim distribution satisfies the new better/worse than used property. We show that some of the examined lower and upper bounds of Ψ may coincide with the exact values of the considered probability.

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Non-exponential bounds for stop-loss premiums and ruin probabilities

Cited by 14 publications

References 6 publications

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

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

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

General bounds for the deficit distribution at ruin in the Sparre Andersen model

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