Correlation order, merging and diversification

Dhaene, Jan; Denuit, Michel; Vanduffel, Steven

doi:10.1016/j.insmatheco.2009.07.007

Cited by 19 publications

(12 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, an increase in the strength of dependence reduces the diversification effect, which makes intuitive sense since higher β values imply that the risks are more positively dependent, i.e., closer to be comonotonic. We refer the reader to Dhaene et al (2009), who investigated the influence of the dependence between losses on the diversification benefit that arises from merging these losses.…”

Section: Simulation Study and Numerical Resultsmentioning

confidence: 99%

Asymptotics for risk capital allocations based on Conditional Tail Expectation

Asimit

Furman

Tang

et al. 2011

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

Abstract. An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-atRisk (VaR) risk measure. The existing methodology acquired for VaR can therefore be applied to a somewhat less well-studied CTE. In the context of interest, the EVT approach is seemingly well-motivated by modern regulations, which openly strive for the excessive prudence in determining risk capitals.

show abstract

Section: Simulation Study and Numerical Resultsmentioning

confidence: 99%

Asymptotics for risk capital allocations based on Conditional Tail Expectation

Asimit

Furman

Tang

et al. 2011

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

show abstract

“…Let us first consider the general proportional allocation principle , where ρ is assumed to be law invariant, translation invariant, and positive homogeneous. In this case, all can be expressed as where z p is the p th quantile of Z for some fixed probability level p ∈ (0, 1) (see, e.g., Dhaene et al, 2009). This means that under the stated conditions, the proportional allocation principle reduces to the haircut allocation principle .…”

mentioning

confidence: 99%

Optimal Capital Allocation Principles

Dhaene¹,

Tsanakas

Valdez

et al. 2011

J of Risk & Insurance

Self Cite

206

160

View full text Add to dashboard Cite

This article develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimization argument, requiring that the weighted sum of measures for the deviations of the business unit's losses from their respective allocated capitals be minimized. The approach is fair insofar as it requires capital to be close to the risk that necessitates holding it. The approach is additionally very flexible in the sense that different forms of the objective function can reflect alternative definitions of corporate risk tolerance. Owing to this flexibility, the general framework reproduces several capital allocation methods that appear in the literature and allows for alternative interpretations and possible extensions.

show abstract

“…Dhaene et al (2009a) investigate the influence of the dependence between random losses on the shortfall and on the diversification benefit that arises from merging these losses. They prove that increasing the dependence between losses, expressed in terms of correlation order, has an 12 increasing effect on the shortfall, expressed in terms of an appropriate integral stochastic order.…”

Section: Risk Measures and Risk Sharingmentioning

confidence: 99%

Advanced Mathematical Methods for Finance

Nunno¹,

Øksendal²

2011

View full text Add to dashboard Cite

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 ) ∈ ...

show abstract

Correlation order, merging and diversification

Cited by 19 publications

References 14 publications

Asymptotics for risk capital allocations based on Conditional Tail Expectation

Asymptotics for risk capital allocations based on Conditional Tail Expectation

Optimal Capital Allocation Principles

Advanced Mathematical Methods for Finance

Contact Info

Product

Resources

About