Optimal hedging with variational preferences under convex risk measures

TL;DR

This paper develops a theoretical framework for optimal hedging using variational preferences and convex risk measures, analyzing properties, dual representations, and pricing conditions to enhance risk management strategies.

Contribution

It introduces a general dual representation for risk-utility composition and studies the convexity and monotonicity of the optimization problem, providing new insights into hedging under risk preferences.

Findings

Establishes a dual representation for risk-utility composition.

Shows the convexity and monotonicity of the hedging optimization map.

Derives conditions for optimality and indifference pricing.

Abstract

We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the optimization problem as a convex and monotone map per se. We also derive results for optimality and indifference pricing conditions. We also explore particular examples inside our setup.