Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs

TL;DR

This paper develops a duality-based method for indifference pricing of contingent claims in discrete time models with proportional transaction costs, using exponential disutility, providing efficient numerical procedures for pricing and trading strategies.

Contribution

It introduces a dual representation and dynamic solution procedure for indifference pricing under exponential disutility with transaction costs, extending utility maximisation methods.

Findings

Provides a convergent numerical method for indifference pricing

Applies to a wide range of payoffs and transaction costs

Offers a dynamic approach for optimal trading strategies

Abstract

We consider indifference pricing of contingent claims consisting of payment flows in a discrete time model with proportional transaction costs and under exponential disutility. This setting covers utility maximisation as a special case. A dual representation is obtained for the associated disutility minimisation problem, together with a dynamic procedure for solving it. This leads to efficient and convergent numerical procedures for indifference pricing, optimal trading strategies and shadow prices that apply to a wide range of payoffs, a large range of time steps and all magnitudes of transaction costs.