A Reconciliation of the Top-Down and Bottom-Up Approaches to Risk Capital Allocations: Proportional Allocations Revisited

Furman, Edward; Kye, Yisub; Su, Jianxi

doi:10.1080/10920277.2020.1774781

Cited by 10 publications

(4 citation statements)

References 45 publications

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“…The class of multivariate probability distributions that admit the stochastic representation described in Proposition 4 is called the class of Liouville distributions, and these distributions are one way to extend the multivariate Dirichlet distribution to the unbounded domain, R n + . Another way is via the class of mixed-Gamma (MG) distributions, which has recently been presented and studied in Furman et al (2020b). Speaking briefly and avoiding unnecessary technicalities -thus considering the simplest possible case -the loss RV X = (X 1 , .…”

Section: Examples and Further Elaborationsmentioning

confidence: 99%

“…We note in passing that a similar reformulation of the RC allocation exercise in the context of the n-dimensional simplex space can be achieved effortlessly for the whole class of weighted RC allocation rules (Furman and Zitikis, 2008b), which are induced by the class of weighted risk measures (Furman and Zitikis, 2008a) and of which allocation rule (1) is a special case (Furman et al, 2020b).…”

Section: Introductionmentioning

confidence: 99%

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Some Results on the Risk Capital Allocation Rule Induced by the Conditional Tail Expectation Risk Measure

Mohammed

Furman

2021

SSRN Journal

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Section: Examples and Further Elaborationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some Results on the Risk Capital Allocation Rule Induced by the Conditional Tail Expectation Risk Measure

Mohammed

Furman

2021

SSRN Journal

Self Cite

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“…There is an extensive amount of studies in the literature dealing with capital allocation problems. Examples of capital allocation problems can be found, for instance, in asset allocation strategies for portfolio selection [14][15][16][17][18][19], the allocation of the total solvency capital requirement across business lines [20][21][22][23], or when distributing total claim costs across the coverage of an insurance policy [24], among others. A comparative analysis of alternative capital allocation principles can be found in Xu and Hu [25] and Balog et al [26].…”

Section: Introductionmentioning

confidence: 99%

Haircut Capital Allocation as the Solution of a Quadratic Optimisation Problem

Belles-Sampera,

Guillen,

Santolino

2023

Mathematics

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The capital allocation framework presents capital allocation principles as solutions to particular optimisation problems and provides a general solution of the quadratic allocation problem via a geometric proof. However, the widely used haircut allocation principle is not reconcilable with that optimisation setting. Our study complements and generalises the unified capital allocation framework. The goal of the study is to contribute in the following two ways. First, we provide an alternative proof of the quadratic allocation problem based on the Lagrange multipliers method to reach the general solution, which complements the geometric proof. This alternative approach to solve the quadratic optimisation problem is, in our opinion, easier to follow and understand by researchers and practitioners. Second, we show that the haircut allocation principle can be accommodated by the optimisation setting with the quadratic optimisation criterion if one of the original conditions is relaxed. Two examples are provided to illustrate the accommodation of this allocation principle.

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“…From a practical point of view, it is also important to be able to fit the multivariate distributions to data using algorithms that can be easily implemented. Examples of multivariate distributions that have enjoyed success in some or all of these aspects include mixed Erlang [52,72] (which is also related to joining exponential, Erlang or mixed Erlang marginal distributions via the Farlie-Gumbel-Morgenstern copula or Sarmanov's family [20,22,62]), gamma [37,36], Pareto [6,64], elliptical [69,38,50,51], and phase-type [19].…”

Section: Introductionmentioning

confidence: 99%

Multivariate matrix-exponential affine mixtures and their applications in risk theory

Cheung¹,

Peralta²,

Woo³

2022

Preprint

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In this paper, a class of multivariate matrix-exponential affine mixtures with matrixexponential marginals is proposed. The class is shown to possess various attractive properties such as closure under size-biased Esscher transform, order statistics, residual lifetime and higher order equilibrium distributions. This allows for explicit calculations of various actuarial quantities of interest. The results are applied in a wide range of actuarial problems including multivariate risk measures, aggregate loss, large claims reinsurance, weighted premium calculations and risk capital allocation. Furthermore, a multiplicative background risk model with dependent risks is considered and its capital allocation rules are provided as well. We finalize by discussing a calibration scheme based on complete data and potential avenues of research.

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A Reconciliation of the Top-Down and Bottom-Up Approaches to Risk Capital Allocations: Proportional Allocations Revisited

Cited by 10 publications

References 45 publications

Some Results on the Risk Capital Allocation Rule Induced by the Conditional Tail Expectation Risk Measure

Some Results on the Risk Capital Allocation Rule Induced by the Conditional Tail Expectation Risk Measure

Haircut Capital Allocation as the Solution of a Quadratic Optimisation Problem

Multivariate matrix-exponential affine mixtures and their applications in risk theory

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