Optimal cross hedging for insurance derivatives

TL;DR

This paper develops optimal cross hedging strategies for insurance derivatives linked to physical risks, using a correlated financial asset to reduce risk and determine indifference prices under exponential utility.

Contribution

It derives explicit optimal strategies and indifference prices for insurance derivatives in a correlated asset framework, incorporating diversification effects and risk reduction via dynamic hedging.

Findings

Dynamic hedging reduces risk aversion by a factor related to correlation.

Optimal strategies depend on the correlation between physical risk and financial asset.

Indifference prices reflect diversification pressure and risk reduction.

Abstract

We consider insurance derivatives depending on an external physical risk process, for example a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal strategies for exponential utility from terminal wealth, determine the indifference prices of the derivatives, and interpret them in terms of diversification pressure. Moreover we check the optimal investment strategies for standard admissibility criteria. Finally we compare the static risk connected with an insurance derivative to the reduced risk due to a dynamic investment into the correlated asset. We show that dynamic hedging reduces the risk aversion in terms of entropic risk measures by a factor related to the correlation.