Risk exchange under infinite-mean Pareto models

TL;DR

This paper investigates how agents make risk-sharing decisions under extremely heavy-tailed Pareto loss distributions, revealing that non-diversification can be optimal and that risk transfer can benefit all parties in such settings.

Contribution

It demonstrates that under super-Pareto losses, diversification is not always optimal and provides an equilibrium analysis of risk exchange markets with heavy-tailed risks.

Findings

Agents prefer non-diversification with super-Pareto losses.

Risk sharing is limited as agents with super-Pareto losses do not share risks.

Risk transfer can improve outcomes for all parties involved.

Abstract

We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are super-Pareto distributions, which include the class of extremely heavy-tailed Pareto distributions. Using a recent result on stochastic dominance, we show that for a portfolio of super-Pareto losses, non-diversification is preferred by decision makers equipped with well-defined and monotone risk measures. The phenomenon that diversification is not beneficial in the presence of super-Pareto losses is further illustrated by an equilibrium analysis in a risk exchange market. First, agents with super-Pareto losses will not share risks in a market equilibrium. Second, transferring losses from agents bearing super-Pareto losses to external parties without any losses may arrive at an equilibrium which benefits every party involved.