On Capital Allocation for a Risk Measure Derived from Ruin Theory

TL;DR

This paper develops new methods for allocating capital based on a dynamic VaR measure derived from ruin theory, ensuring low ruin probability with practical properties and comparisons to existing methods.

Contribution

It introduces a novel, intuitive allocation method for ruin-based risk measures and analyzes its properties and performance relative to existing approaches.

Findings

The new allocation method satisfies desirable theoretical properties.

Comparison shows advantages over gradient allocation in certain scenarios.

Examples demonstrate practical applicability and effectiveness.

Abstract

This paper addresses allocation methodologies for a risk measure inherited from ruin theory. Specifically, we consider a dynamic value-at-risk (VaR) measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given threshold. We introduce an intuitively appealing, novel allocation method, with a focus on its application to capital reserves which are determined through the dynamic value-at-risk (VaR) measure. Various desirable properties of the presented approach are derived including a limit result when considering a large time horizon and the comparison with the frequently used gradient allocation method. In passing, we introduce a second allocation method and discuss its relation to the other allocation approaches. A number of examples illustrate the applicability and performance of the allocation approaches.