Efficient Approximations for Utility-Based Pricing

Laurence Carassus () and Massinissa Ferhoune ()
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Laurence Carassus: Laboratoire de Mathématiques de Reims, UMR9008 CNRS et Université de Reims Champagne-Ardenne
Massinissa Ferhoune: Laboratoire de Mathématiques de Reims, UMR9008 CNRS et Université de Reims Champagne-Ardenne

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 2, 1-38

Abstract: Abstract In a context of illiquidity, the reservation price is a well-accepted alternative to the usual martingale approach which does not apply. However, this price is not available in closed form and requires numerical methods such as Monte Carlo or polynomial approximations to evaluate it. We show that these methods can be inaccurate and propose a deterministic decomposition of the reservation price using the Lambert function. This decomposition allows us to perform an improved Monte Carlo method, which we name Lambert Monte Carlo (LMC) and to give deterministic approximations of the reservation price and of the optimal strategies based on the Lambert function. We also give an answer to the problem of selecting a hedging asset that minimizes the reservation price and also the cash invested. Our theoretical results are illustrated by numerical simulations.

Keywords: Utility-based pricing; Utility-based hedging; Incomplete model; Monte Carlo method; 91G20; 91G60; 60E10; 90-04 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11009-024-10076-z

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