Restricted Entropic and Quadratic Hedging in the Small-Risk-Aversion Limit

By Jonas Hanetho

Rating

1860
Battle Count: 51

Relevance

7/10
Highly relevant for quantitative researchers and practitioners dealing with hedging in incomplete markets. It provides theoretical justification for using quadratic hedging as an approximation for entropic hedging when risk aversion is low, which is common in practical numerical implementations where computational efficiency is key.

Implementation Complexity

6/10
The theoretical framework requires understanding of functional analysis (compactness, convexity in L2) and stochastic calculus. The numerical implementation involves simulating a modified Heston model with truncation and compensation, which is moderately complex but standard in computational finance.

Reproducibility

3/5
The paper provides a fully specified simulation model (truncated compensated Heston-type) and detailed mathematical proofs. However, no public code repository URL is explicitly provided in the text extract, though the methodology is described sufficiently for re-implementation by an expert.

Abstract

In incomplete markets, contingent claims cannot in general be replicated exactly, and hedging must therefore be formulated as an optimization problem over admissible trading strategies. This paper studies the relation between quadratic hedging and entropic hedging in a discrete-time incomplete market when strategies are restricted to bounded finite-dimensional parametric classes. These restrictions induce admissible gain sets that are compact and convex in \(L^2\), providing a common well-posed setting for both the restricted mean-square hedging problem and the restricted exponential-utility hedging problem. The main contribution is to establish a uniform small-risk-aversion expansion of the entropic risk functional over the restricted gain set and to use this uniformity to obtain convergence of the corresponding minimizers. Under a uniform exponential integrability assumption, the restricted entropic hedging gains converge in \(L^2\) to the unique restricted quadratic hedge as the risk-aversion parameter tends to zero. The theoretical result is illustrated numerically in a regularized discrete-time stochastic volatility model of Heston type.

Links

arXiv:2610.12594 ยท Paper rankings

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