Insurance Risk, Risk Measures, and Capital Allocation: Navigating a Copernican Shift

2013 ◽  
Vol 5 (1) ◽  
pp. 201-223 ◽  
Author(s):  
Michael R. Powers ◽  
George Zanjani
Keyword(s):  
Risk Measures ◽  
Capital Allocation ◽  
Insurance Risk

CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH

2019 ◽  
Vol 34 (2) ◽  
pp. 297-315
Author(s):  
Linxiao Wei ◽  
Yijun Hu
Keyword(s):  
Standard Deviation ◽  
Portfolio Management ◽  
Risk Measures ◽  
Risk Measure ◽  
Axiomatic Approach ◽  
Capital Allocation ◽  
Axiom System ◽  
Multivariate Risk ◽  
Multivariate Risk Measures ◽  
Multivariate Risk Measure

AbstractCapital allocation is of central importance in portfolio management and risk-based performance measurement. Capital allocations for univariate risk measures have been extensively studied in the finance literature. In contrast to this situation, few papers dealt with capital allocations for multivariate risk measures. In this paper, we propose an axiom system for capital allocation with multivariate risk measures. We first recall the class of the positively homogeneous and subadditive multivariate risk measures, and provide the corresponding representation results. Then it is shown that for a given positively homogeneous and subadditive multivariate risk measure, there exists a capital allocation principle. Furthermore, the uniqueness of the capital allocation principe is characterized. Finally, examples are also given to derive the explicit capital allocation principles for the multivariate risk measures based on mean and standard deviation, including the multivariate mean-standard-deviation 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.

CAPITAL ALLOCATION FOR SET-VALUED RISK MEASURES

2020 ◽  
Vol 23 (01) ◽  
pp. 2050009
Author(s):  
FRANCESCA CENTRONE ◽  
EMANUELA ROSAZZA GIANIN
Keyword(s):  
Convex Set ◽  
Risk Measures ◽  
Risk Measure ◽  
Capital Allocation ◽  
Allocation Rule ◽  
Scalar Case ◽  
Representation Theorems ◽  
Allocation Rules ◽  
The One ◽  
Definition Of

We introduce the definition of set-valued capital allocation rule, in the context of set-valued risk measures. In analogy to some well known methods for the scalar case based on the idea of marginal contribution and hence on the notion of gradient and sub-gradient of a risk measure, and under some reasonable assumptions, we define some set-valued capital allocation rules relying on the representation theorems for coherent and convex set-valued risk measures and investigate their link with the notion of sub-differential for set-valued functions. We also introduce and study the set-valued analogous of some properties of classical capital allocation rules, such as the one of no undercut. Furthermore, we compare these rules with some of those mostly used for univariate (single-valued) risk measures. Examples and comparisons with the scalar case are provided at the end.

scholarly journals Marginal Decomposition of Risk Measures

2006 ◽  
Vol 36 (2) ◽  
pp. 375-413
Author(s):  
Gary G. Venter ◽  
John A. Major ◽  
Rodney E. Kreps
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Directional Derivative ◽  
Component Composition ◽  
Capital Allocation ◽  
Directional Derivatives ◽  
Total Risk ◽  
Business Decision ◽  
Marginal Risk

The marginal approach to risk and return analysis compares the marginal return from a business decision to the marginal risk imposed. Allocation distributes the total company risk to business units and compares the profit/risk ratio of the units. These approaches coincide when the allocation actually assigns the marginal risk to each business unit, i.e., when the marginal impacts add up to the total risk measure. This is possible for one class of risk measures (scalable measures) under the assumption of homogeneous growth and by a subclass (transformed probability measures) otherwise. For homogeneous growth, the allocation of scalable measures can be accomplished by the directional derivative. The first well known additive marginal allocations were the Myers-Read method from Myers and Read (2001) and co-Tail Value at Risk, discussed in Tasche (2000). Now we see that there are many others, which allows the choice of risk measure to be based on economic meaning rather than the availability of an allocation method. We prefer the term “decomposition” to “allocation” here because of the use of the method of co-measures, which quantifies the component composition of a risk measure rather than allocating it proportionally to something.Risk adjusted profitability calculations that do not rely on capital allocation still may involve decomposition of risk measures. Such a case is discussed. Calculation issues for directional derivatives are also explored.

scholarly journals Portfolio optimization by using MeanSharp-βVaR and Multi Objective MeanSharp-βVaR models

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 815-823
Author(s):  
Shokoofeh Banihashemi ◽  
Sarah Navidi
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Risk Measures ◽  
Capital Allocation ◽  
Second Step ◽  
Data Envelopment ◽  
Negative Data ◽  
Multi Objective ◽  
Dea Models ◽  
Inputs And Outputs

The purpose of this study is to develop portfolio optimization and assets allocation using our proposed models. For this, three steps are considered. In the first step, the stock companies screen by their financial data. For second step, we need some inputs and outputs for solving Data Envelopment Analysis (DEA) models. Conventional DEA models assume non-negative data for inputs and outputs. However, many of these data take the negative value, therefore we propose the MeanSharp-?VaR (MSh?V) model and the Multi Objective MeanSharp-?VaR (MOMSh?V) model based on Range Directional Measure (RDM) that can take positive and negative values. Also, we consider one of downside risk measures named Value at Risk (VaR) and try to decrease it. After using our proposed models, the efficient stock companies will be selected for making the portfolio. In the third step, Multi Objective Decision Making (MODM) model was used to specify the capital allocation to the stock companies that was selected for the portfolio. Finally, a numerical example of the purposed method in Iranian stock companies is presented.

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.

scholarly journals The Implementation of Asset Allocation Approaches: Theory and Evidence

2020 ◽  
Vol 12 (17) ◽  
pp. 7162
Author(s):  
Jung-Bin Su
Keyword(s):  
Asset Allocation ◽  
Risk Measures ◽  
Traditional Approach ◽  
Selection Criterion ◽  
Efficient Frontier ◽  
Capital Allocation ◽  
Currency Markets ◽  
Volatility Risk ◽  
Forecast Performance ◽  
Asset Selection

This study develops three capital allocation approaches and a directional weight increment algorithm to identify the efficient frontier of all possible multi-asset portfolios precisely and rapidly. Subsequently, this study proposes an asset selection criterion, based on the coefficient of variance and volatility risk measures, to perform the asset allocation for two types of investors who are willing or not willing to bear the risk. Finally, this study uses a multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model to estimate the conditional variance and covariance of several multi-asset portfolios constituted of seven assets dispersed in the oil, stock, and currency markets of the US. The empirical results show that, via applying the proposed asset selection criterion, the most suitable multi-asset portfolios are the SP500-Nasdaq and the GasNyh-DJ, which belong to the relatively most efficient portfolios. Moreover, two capital allocation approaches using the entire sample weight forecasts have the best forecast performance. Additionally, for all multi-asset portfolios the weight combination set of portfolios on the efficient frontier that resulted from the proposed algorithm is consistent with that obtained from the traditional approach.

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