Does positive dependence between individual risks increase stop-loss premiums?

Denuit, Michel; Dhaene, Jan; Ribas, Carme Besson

doi:10.1016/s0167-6687(00)00079-2

Cited by 58 publications

(27 citation statements)

References 12 publications

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“…We first investigate the effect of exchangeability, among direct defaults and among infections, on the total defaults' number evolution. This kind of impact is also dealt with by Denuit, Dhaene and Ribas (2001) and Denuit, Lefèvre and Utev (2002) in a life insurance framework, and it appears that some quantitative measures could be notably affected by dependencies among the considered random variables. Here, we will be concerned about the impact of such dependencies on the first moments of total defaults' number N t and on the survival function of N t at some points.…”

Section: Numerical Applicationsmentioning

confidence: 99%

An extension of Davis and Lo's contagion model

Rullière¹,

Dorobantu²,

Cousin³

2013

Quantitative Finance

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: The present paper provides a multi-period contagion model in the credit risk field. Our model is an extension of Davis and Lo's infectious default model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). The spontaneous default without external influence and the infections are described by not necessarily independent Bernoulli-type random variables. Moreover, several contaminations could be required to infect another firm. In this paper we compute the probability distribution function of the total number of defaults in a dependency context. We also give a simple recursive algorithm to compute this distribution in an exchangeability context. Numerical applications illustrate the impact of exchangeability among direct defaults and among contaminations, on different indicators calculated from the law of the total number of defaults. We then calibrate the model on iTraxx data before and during the crisis. The dynamic feature together with the contagion effect have a significant impact on the model performance, especially during the recent distressed period.

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Section: Numerical Applicationsmentioning

confidence: 99%

An extension of Davis and Lo's contagion model

Rullière¹,

Dorobantu²,

Cousin³

2013

Quantitative Finance

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“…Goovaerts (1996, 1997), Müller (1997), Bäuerle and Müller (1998), Wang and Dhaene (1998), Goovaerts and Dhaene (1999) and Denuit et al (2001) generalize (6) by investigating how changing the dependence structure of an insurance portfolio influences its stop-loss premiums. In any of the different situations considered in these papers, the convex order relation (6) corresponds with the extreme case where the comonotonic dependence structure is involved.…”

Section: Convex Bounds For Sums Of Random Variablesmentioning

confidence: 99%

Advanced Mathematical Methods for Finance

Nunno¹,

Øksendal²

2011

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Over the last decade, it has been shown that the concept of comonotonicity is a helpful tool for solving several research and practical problems in the domain of finance and insurance. In this paper, we give an extensive bibliographic overview -without claiming to be complete -of the developments of the theory of comonotonicity and its applications, with an emphasis on the achievements over the last five years. These applications range from pricing and hedging of derivatives over risk management to life insurance. ComonotonicityOver the last two decades, researchers in economics, financial mathematics and actuarial science have introduced results related to the concept of comonotonicity in their respective fields of interest. In this paper, we give an overview of the relevant literature in these research fields, with the main emphasis on the development of the theory and its applications in finance and insurance over the last five years. Although it is our intention to give an extensive bibliographic overview, due to the high number of papers on applications of comonotonicity, it is impossible to present here an exhaustive overview of the recent literature. Further, we restrict this paper to a description of how and where comonotonicity comes in and refer to the relevant papers for a detailed mathematical description. In order to make this paper self-contained, we also provide a short overview of the basic definitions and initial main results of comonotonicity theory, hereby referring to part of the older literature on this topic.The concept of comonotonicity is closely related to the following well-known result, which is usually attributed to both Hoeffding (1940) and Fréchet (1951): For any n-dimensional random vector X ≡ (X 1 , X 2 , . . . , X n ) with multivariate cumulative distribution function (cdf) F X and marginal univariate cdf's F X 1 , F X 2 , . . . , F Xn and for any x ≡ (x 1 , x 2 , . . . , x n ) ∈ R n it holds that F X (x) ≤ min (F X 1 (x 1 ) , F X 2 (x 2 ) , . . . , F Xn (x n )) .(1)In the sequel, the notation R n (F X 1 , F X 2 , . . . , F Xn ) will be used to denote the class of all random vectors Y ≡ (Y 1 , Y 2 , . . . , Y n ) with marginals F Y i equal to the respective marginals F X i . The set R n (F X 1 , F X 2 , . . . , F Xn ) is called the Fréchet class related to the random vector X.The upper bound in (1) is reachable in the Fréchet class R n (F X 1 , F X 2 , . . . , F Xn ) in the sense that it is the cdf of an n-dimensional random vector with marginals given by F X i , i = 1, 2, . . . , n. * Department of Mathematics, ECARES, Université Libre de Bruxelles, CP 210, 1050 Brussels, Belgium † Faculty of Business and Economics, Katholieke Universiteit, 3000 Leuven, Belgium. ‡ Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, 9000 Gent, Belgium 1 In order to prove the reachability property, consider a random variable U , uniformly distributed on the unit interval (0, 1). Then one has that F −1 X 1 (U ), F −1 X 2 (U ), . . . , F −1 Xn (U ) ∈ ...

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“…The extreme dependence structures that can be used are two dependence concepts: comonotonicity and countermonotonicity. The theory behind these concepts is extensively presented in [23], [24], [25], while the application in power systems has been presented by the authors in a number of recent papers [21], [26], [27].…”

Section: Extreme Stochastic Dependence Modelling: Stochastic Boundsmentioning

confidence: 99%

Integration of stochastic generation in power systems

Papaefthymiou

Schavemaker

Sluis

et al. 2006

International Journal of Electrical Power & Energy Systems

147

103

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-Stochastic generation, i.e. electrical power production by an uncontrolled primary energy source, is expected to play an important role in future power systems. A new power system structure is created due to the largescale implementation of this small-scale, distributed, nondispatchable generation; the 'horizontally operated' system. Modelling methodologies that can deal with the operational uncertainty introduced by these power units should be used for analyzing the impact of this generation to the system. In this contribution, the principles for this modelling are presented, based on the decoupling of the single stochastic generator behavior (marginal distribution-stochastic unit capacity) from the concurrent behavior of the stochastic generators (stochastic dependence structure-stochastic system dispatch). Subsequently, the Stochastic Bounds Methodology is applied to model the extreme power contribution of the stochastic generation to the system, based on two new sampling concepts (comonotonicity-countermonotonicity). The application of this methodology to the power system leads to the definition of clusters of positively correlated stochastic generators and the combination of different clusters based on the sampling concepts. The stochastic decomposition and clustering concepts presented in this contribution give the basis for the application of new uncertainty analysis techniques, for the modelling of the stochastic generation in power systems.

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Does positive dependence between individual risks increase stop-loss premiums?

Cited by 58 publications

References 12 publications

An extension of Davis and Lo's contagion model

An extension of Davis and Lo's contagion model

Advanced Mathematical Methods for Finance

Integration of stochastic generation in power systems

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