Scaling Limits for Exponential Hedging in the Brownian Framework

2025/02/24 by Yan Dolinksy, Xin Zhang, Dolinksy, Yan +1
Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2502.17186

openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

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