Scaling Limits for Exponential Hedging in the Brownian Framework

TL;DR

This paper investigates the asymptotic behavior of exponential utility indifference prices in a Brownian model, linking scaling limits to relative entropy and constructing optimal hedging strategies.

Contribution

It introduces a novel connection between scaling limits of exponential prices and specific relative entropy, and develops asymptotic optimal hedging strategies in the continuous-time setting.

Findings

Scaling limits characterized by specific relative entropy

Existence of classical solutions to the HJB equation

Construction of asymptotically optimal hedging strategies

Abstract

In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy}, and in addition we construct asymptotic optimal hedging strategies. To prove the upper bound for the limit, we formulate the dual problem as a stochastic control, and show there exists a classical solution to its Hamilton-Jacobi-Bellman (HJB) equation. The proof for the lower bound relies on the duality result for exponential hedging in discrete time.