On excess of loss reinsurance with reinstatements

Sundt, Bjørn

doi:10.1016/0167-6687(93)91027-r

Cited by 13 publications

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“…In practice, there is often an upper limit of coverage in terms of m reinstatements of the i-th partner in the reinsurance chain; i.e., the actual coverage is given by X i (t) = min{X i (t), mv i } with m ∈ N. Most of the results in the literature on fair pricing of reinstatement contracts are based on the assumption that the claim number process N (t) is in the Sundt-Jewell class (see for instance Sundt [22] or Mata [14]). The results in this paper in principle allow us to extend this type of analysis to more general situations.…”

Section: The Sundt-jewell Classmentioning

confidence: 99%

On excess-of-loss reinsurance

Albrecher

Teugels

2009

Theor. Probability and Math. Statist.

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Abstract. We discuss a unified framework to analyze the distribution of the number of claims and the aggregate claim sizes in an excess-of-loss reinsurance contract based upon the use of point processes and work out several examples explicitly. We first deal with a single excess-of-loss situation with an extra upper bound on the coverage of individual claims. Subsequently the results are extended to a reinsurance chain with k partners. IntroductionTraditionally, an excess-of-loss reinsurance form covers the overshoot over a certain retention level M for all claims whether or not they are considered to be large. Among the insurance branches where it is used, we mention in particular general liability, and to a lesser extent motor liability ([25]) and windstorm reinsurance ([18]). Because of its transparency, an excess-of-loss treaty has been one of the main research objects in the reinsurance literature right from the beginning (see for instance [3,4]). It is clear that excess-of-loss reinsurance limits the liability of the first line insurer but that he himself will cover all claims below the retention M . In this form, the excess-of-loss reinsurance treaty cover has a number of desirable theoretical properties as explained by Bühlmann in [5] and by Asmussen et al. in [2]. For a combination with quota-share reinsurance, see [6].We will look at a more general form where each claim will be considered between two boundaries: we will call the lower retention u while the upper will be taken to be u + v, indicating by v the range for which the treaty is used. As illustrated below, the notation allows us to deal with any partner in an excess-loss reinsurance chain. If u and v depend on the claim orderings, then this reinsurance form is commonly called drop-down-excessof-loss reinsurance. For a study of such a reinsurance form, we refer to Ladoucette et al. [12].In the following we need some basic notation, first for the original portfolio.• The epochs of the claims are denoted by T 0 = 0, T 1 , T 2 , . . . . Apart from the fact that the epochs form a nondecreasing sequence, we in general do not assume anything specific about their interdependence. The random variables defined by W 0 = 0 and {W i+1 := T i+1 − T i ; i = 0, 1, . . .} are called the waiting times in between successive claims. In some particular cases it might be useful to assume that the sequence {W i ; i ≥ 1} consists of independent random variables all with a common distribution V as a random variable T , i.e. P(T ≤ x) = V (x). In that2000 Mathematics Subject Classification. Primary 62P05, 62H20.

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Section: The Sundt-jewell Classmentioning

confidence: 99%

On excess-of-loss reinsurance

Albrecher

Teugels

2009

Theor. Probability and Math. Statist.

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“…Generally, reinstatement percentages are fixed in advance: this assumption moves our attention to the study of the initial premium defined by local equilibrium condition (9). From now on we make the assumption that the premium for the i-th reinstatement (5) is a twopoint random variable distributed as c i P B p i and B p i denotes a Bernoulli random variable such that P r[…”

Section: Initial Premiums and Limit On The Payment Of Each Claimmentioning

confidence: 99%

“…Now we turn our attention to the analysis of local equilibrium condition (9) and in order to consider the case of generalized risk adjusted premium principle we define and study the following generalized local equilibrium condition…”

Section: Generalized Initial Premiums and Exchangeabilitymentioning

confidence: 99%

“…The excess of loss reinsurance model we study in this paper is related to the model that has been originally proposed and analyzed by Sundt [9] and that it has been subsequently generalized (see [1] and [3]). Given the initial premium P , the limit on the payment of each claim m, the number of reinstatements K (such that the aggregate limit M satisfies M = (K + 1)m), the aggregate deductible D, the percentages of reinstatement c i , (i = 1, .…”

Section: Introductionmentioning

confidence: 99%

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Initial premium, aggregate claims and distortion risk measures in XL reinsurance with reinstatements

Campana

Ferretti

2012

Mathematical and Statistical Methods for Actuarial Sciences and Finance

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Abstract. With reference to risk adjusted premium principle, in this paper we study excess of loss reinsurance with reinstatements in the case in which the aggregate claims are generated by a discrete distribution. In particular, we focus our study on conditions ensuring feasibility of the initial premium, for example with reference to the limit on the payment of each claim. Comonotonic exchangeability shows the way forward to a more general definition of the initial premium: some properties characterizing the proposed premium are presented.

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“…The main papers on the subject have been Simon(1972) and Sundt(1991). More recent discussions include Walhin(2001Walhin( /2002, Paris(2000/2001a/b), Mata(2000), Hess and Schmidt(2004).…”

Section: Introductionmentioning

confidence: 99%

Excess of Loss Reinsurance with Reinstatements Revisited

Hürlimann¹

2005

ASTIN Bull.

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The classical evaluation of pure premiums for excess of loss reinsurance with reinstatements requires the knowldege of the claim size distribution of the insurance risk. In the situation of incomplete information, where only a few characteristics of the aggregate claims to an excess of loss layer can be estimated, the method of stop-loss ordered bounds yields a simple analytical distribution-free approximation to pure premiums of excess of loss reinsurance with reinstatements. It is shown that the obtained approximation is enough accurate for practical purposes and improves the analytical approximations obtained using either a gamma, translated gamma, translated inverse Gaussian or a mixture of the last two distributions.

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On excess of loss reinsurance with reinstatements

Cited by 13 publications

References 0 publications

On excess-of-loss reinsurance

On excess-of-loss reinsurance

Initial premium, aggregate claims and distortion risk measures in XL reinsurance with reinstatements

Excess of Loss Reinsurance with Reinstatements Revisited

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