Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits

TL;DR

This paper models the loss distributions of financial agents sharing light-tailed claims, revealing how diversification impacts risk during crises, with explicit formulas for conditional losses under exponential claim assumptions.

Contribution

It introduces a novel analysis of light-tailed claim sharing, deriving explicit loss distributions and a criterion for diversification benefits during systemic stress.

Findings

Losses follow generalized exponential mixture distributions.

Diversification can reduce risk in crisis scenarios under certain conditions.

Explicit formulas for conditional loss distributions are provided.

Abstract

We analyze systems of agents sharing light-tailed risky claims issued by different financial objects. Assuming exponentially distributed claims, we obtain that both agents' and system's losses follow generalized exponential mixture distributions. We show that this leads to qualitatively different results on individual and system risks compared to heavy-tailed claims previously studied in the literature. By deducing conditional loss distributions we investigate the impact of stress situations on agents' and system's losses. Moreover, we present a criterion for agents to decide whether holding few objects or portfolio diversification minimizes their risks in system crisis situations.