A Note on the Net Premium for a Generalized Largest Claims Reinsurance Cover

Berglund, Raoul M

doi:10.2143/ast.28.1.519084

Cited by 9 publications

(10 citation statements)

References 9 publications

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“…A series of approximate premium calculations for LCR treaties has been made in the literature; see, for example, [15,16], and [17][18][19][20], and their references.…”

Section: Reinsurance Premium and Dividend Adjustmentmentioning

confidence: 99%

The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation

Fan

Griffin

Maller

et al. 2017

Risks

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Abstract:We compare two types of reinsurance: excess of loss (EOL) and largest claim reinsurance (LCR), each of which transfers the payment of part, or all, of one or more large claims from the primary insurance company (the cedant) to a reinsurer. The primary insurer's point of view is documented in terms of assessment of risk and payment of reinsurance premium. A utility indifference rationale based on the expected future dividend stream is used to value the company with and without reinsurance. Assuming the classical compound Poisson risk model with choices of claim size distributions (classified as heavy, medium and light-tailed cases), simulations are used to illustrate the impact of the EOL and LCR treaties on the company's ruin probability, ruin time and value as determined by the dividend discounting model. We find that LCR is at least as effective as EOL in averting ruin in comparable finite time horizon settings. In instances where the ruin probability for LCR is smaller than for EOL, the dividend discount model shows that the cedant is able to pay a larger portion of the dividend for LCR reinsurance than for EOL while still maintaining company value. Both methods reduce risk considerably as compared with no reinsurance, in a variety of situations, as measured by the standard deviation of the company value. A further interesting finding is that heaviness of tails alone is not necessarily the decisive factor in the possible ruin of a company; small and moderate sized claims can also play a significant role in this.

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“…A series of approximate premium calculations for LCR treaties has been made in the literature; see, for example, [15,16], and [17][18][19][20], and their references.…”

Section: Reinsurance Premium and Dividend Adjustmentmentioning

confidence: 99%

The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation

Fan

Griffin

Maller

et al. 2017

Risks

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“…Formulas for E((C N−i+1:N ) k ) and E(C N−i+1:N C N−j+1:N ) have been proposed in several works, especially in that of Berglund (1998). These formulas are recalled hereafter, because they are used in Section 4 to work out our numerical applications and because our own formulas for the cedent's share, although more complex, have similar features.…”

Section: The First Two Moments Of the Reinsured Share In The Lcr And mentioning

confidence: 99%

“…These formulas were used by Berglund (1998) to determine the moments of order 1 and 2 of the above random variables (and the moments of the cross products).…”

Section: Proposition 32 Assume That E(n) and E(cmentioning

confidence: 99%

“…Kremer has considered various situations using several approaches. More recently, Berglund (1998), Walhin (2003), Bathossi (2003), and Ladoucette and Teugels (2006) have also contributed to this subject. Basically, the goal of these authors was the pricing of Largest Claims Reinsurance (LCR) and/or ECOMOR treaties (see Section 2 for the precise definitions).…”

Section: Introductionmentioning

confidence: 99%

“…In particular, calculations or estimations of the first two moments of the reinsurer's claim expenses have been developed. One of the most precise results along this line is certainly that of Berglund (1998), who has established closed and tractable formulas.…”

Section: Introductionmentioning

confidence: 99%

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Computing the mean and the variance of the cedent’s share for largest claims reinsurance covers

Heß

2009

Insurance: Mathematics and Economics

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JEL classification: C65 IM52 IM54 IB90 IB92 Keywords: Largest claims reinsurance Order statistics Extreme value theory Cedent's point of view a b s t r a c tWe present mathematical results allowing one to evaluate the moments of order 1 and 2 of the cedent's share in the framework of reinsurance treaties based on ordered claim sizes. These results consist of closed analytical formulas that do not involve any approximation procedure. This is illustrated by numerical examples when the claim number has the Poisson or the negative binomial distribution, and the claim cost has the exponential or the Pareto distribution.

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2017

Reinsurance

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A Note on the Net Premium for a Generalized Largest Claims Reinsurance Cover

Cited by 9 publications

References 9 publications

The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation

The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation

Computing the mean and the variance of the cedent’s share for largest claims reinsurance covers

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