Risk capital allocation by coherent risk measures based on one-sided moments

2003 ◽  
Vol 32 (1) ◽  
pp. 135-146 ◽  
Author(s):  
T. Fischer
Keyword(s):  
Risk Measures ◽  
Capital Allocation ◽  
Coherent Risk Measures ◽  
Risk Capital ◽  
Coherent Risk ◽  
Risk Capital Allocation

scholarly journals Surplus Sharing with Coherent Utility Functions

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 7
Author(s):  
Delia Coculescu ◽  
Freddy Delbaen
Keyword(s):  
Risk Measures ◽  
Capital Allocation ◽  
Utility Functions ◽  
Coherent Risk Measures ◽  
Coherent Risk ◽  
Surplus Sharing ◽  
Insurance Business

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e., the shareholders.

scholarly journals Fair estimation of capital risk allocation

2020 ◽  
Vol 37 (1-2) ◽  
pp. 1-24
Author(s):  
Tomasz R. Bielecki ◽  
Igor Cialenco ◽  
Marcin Pitera ◽  
Thorsten Schmidt
Keyword(s):  
Numerical Study ◽  
Risk Measures ◽  
Estimation Procedure ◽  
Capital Allocation ◽  
Expected Shortfall ◽  
Substantial Part ◽  
Risk Allocation ◽  
Fair Allocation ◽  
Risk Capital ◽  
Risk Capital Allocation

AbstractIn this paper, we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We introduce the concept of fair capital allocations and provide explicit formulae for fair capital allocations in case when the constituents of the risky portfolio are jointly normally distributed. The main focus of the paper is on the problem of approximating fair portfolio allocations in the case of not fully known law of the portfolio constituents. We define and study the concepts of fair allocation estimators and asymptotically fair allocation estimators. A substantial part of our study is devoted to the problem of estimating fair risk allocations for expected shortfall. We study this problem under normality as well as in a nonparametric setup. We derive several estimators, and prove their fairness and/or asymptotic fairness. Last, but not least, we propose two backtesting methodologies that are oriented at assessing the performance of the allocation estimation procedure. The paper closes with a substantial numerical study of the subject and an application to market data.

Modelling random vectors of dependent risks with different elliptical components

2021 ◽  
pp. 1-19
Author(s):  
Zinoviy Landsman ◽  
Tomer Shushi
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Degrees Of Freedom ◽  
Risk Measures ◽  
Capital Allocation ◽  
Risk Capital ◽  
Dependent Risks ◽  
Risk Capital Allocation ◽  
Elliptical Copula ◽  
T Distribution

Abstract In Finance and Actuarial Science, the multivariate elliptical family of distributions is a famous and well-used model for continuous risks. However, it has an essential shortcoming: all its univariate marginal distributions are the same, up to location and scale transformations. For example, all marginals of the multivariate Student’s t-distribution, an important member of the elliptical family, have the same number of degrees of freedom. We introduce a new approach to generate a multivariate distribution whose marginals are elliptical random variables, while in general, each of the risks has different elliptical distribution, which is important when dealing with insurance and financial data. The proposal is an alternative to the elliptical copula distribution where, in many cases, it is very difficult to calculate its risk measures and risk capital allocation. We study the main characteristics of the proposed model: characteristic and density functions, expectations, covariance matrices and expectation of the linear regression vector. We calculate important risk measures for the introduced distributions, such as the value at risk and tail value at risk, and the risk capital allocation of the aggregated risks.

scholarly journals Surplus Sharing with Coherent Utility Functions

2018 ◽  
Author(s):  
Delia Coculescu ◽  
Freddy Delbaen
Keyword(s):  
Risk Measures ◽  
Capital Allocation ◽  
Utility Functions ◽  
Coherent Risk Measures ◽  
Coherent Risk ◽  
Surplus Sharing ◽  
Insurance Business

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e. the shareholders.

scholarly journals Capital Allocation Rules and the No-Undercut Property

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 175
Author(s):  
Gabriele Canna ◽  
Francesca Centrone ◽  
Emanuela Rosazza Gianin
Keyword(s):  
Risk Measures ◽  
Capital Allocation ◽  
Coherent Risk Measures ◽  
Infinite Games ◽  
Allocation Rules ◽  
Coherent Risk ◽  
Allocation Problems ◽  
The One

This paper makes the point on a well known property of capital allocation rules, namely the one called no-undercut. Its desirability in capital allocation stems from some stability game theoretical features that are related to the notion of core, both for finite and infinite games. We review these aspects, by relating them to the properties of the risk measures that are involved in capital allocation problems. We also discuss some problems and possible extensions that arise when we deal with non-coherent risk measures.

scholarly journals Sharing Risk – An Economic Perspective

2009 ◽  
Vol 39 (2) ◽  
pp. 591-613 ◽  
Author(s):  
Andreas Kull
Keyword(s):  
Value At Risk ◽  
Risk Sharing ◽  
Risk Measures ◽  
Insurance Industry ◽  
Risk Measure ◽  
Capital Allocation ◽  
Risk Capital ◽  
Risk Class ◽  
Capital Costs ◽  
Risk Transfer

AbstractWe revisit the relative retention problem originally introduced by de Finetti using concepts recently developed in risk theory and quantitative risk management. Instead of using the Variance as a risk measure we consider the Expected Shortfall (Tail-Value-at-Risk) and include capital costs and take constraints on risk capital into account. Starting from a risk-based capital allocation, the paper presents an optimization scheme for sharing risk in a multi-risk class environment. Risk sharing takes place between two portfolios and the pricing of risktransfer reflects both portfolio structures. This allows us to shed more light on the question of how optimal risk sharing is characterized in a situation where risk transfer takes place between parties employing similar risk and performance measures. Recent developments in the regulatory domain (‘risk-based supervision’) pushing for common, insurance industry-wide risk measures underline the importance of this question. The paper includes a simple non-life insurance example illustrating optimal risk transfer in terms of retentions of common reinsurance structures.

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