Forward Exponential Performances: Pricing and Optimal Risk Sharing

TL;DR

This paper develops a framework for pricing and risk sharing in financial markets using forward exponential performance processes, extending traditional utility models to a dynamic, forward-looking setting.

Contribution

It introduces a novel approach to contingent claim valuation and optimal risk sharing based on forward exponential utilities, providing new insights and solutions in stochastic volatility models.

Findings

Derived properties of forward exponential indifference valuation

Compared forward and backward exponential utility valuations

Solved the optimal risk sharing problem for exponential forward utilities

Abstract

In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a number of properties are proved and discussed. Special attention is given to the comparison between the forward exponential and the backward exponential utility indifference valuation. In addition, we construct the problem of optimal risk sharing in this forward setting and solve it when the agents' forward performance criteria are exponential.