Abstract
In order to protect stakeholders of insurance companies and financial institutions against adverse outcomes of risky businesses, regulators and senior management use capital allocation techniques. For enterprise-wide risk management, it has become important to calculate the contribution of each risk within a portfolio. For that purpose, bivariate lower and upper orthant tail value-at-risk can be used for capital allocation. In this paper, we present multivariate value-at-risk and tail-value-at-risk for d ≥ 2 , and we focus on three different methods to calculate optimal values for the contribution of each risk within the sums of random vectors to the overall portfolio, which could particularly apply to insurance and financial portfolios.
Highlights
For insurance companies and financial institutions, regulations are established for solvency capital requirements
The multivariate upper orthant TVaR-based contributions can be interpreted as the expected values of a risk Xi,j knowing that its aggregate business unit takes higher values than the aggregate business unit’s upper orthant VaR
We provide a multivariate representation of lower and upper orthant TVaR
Summary
For insurance companies and financial institutions, regulations are established for solvency capital requirements. We present three different methods to select specific sets from the curves, which can be useful for practical purposes The latter situation legitimates the use of multivariate risk measures on which to base capital allocation, as presented . For cases where business units aggregation is not an option, multivariate risk measures are used to allocate capital for components or classes of aggregate risks of the overall portfolio This conservative allocation reflects the uncertainty of our economy and attempts to find a balance between making expected losses and preserving capital for the extreme events. They illustrate different values obtained when changing the dependence structures within and between the lines of business of a portfolio composed of two aggregate classes
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