Utility Maximisation with Model-independent Constraints

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Hauptverfasser: Cox, Alexander M. G., Hernandez-Hernandez, Daniel
Format: Preprint
Veröffentlicht: 2025
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author Cox, Alexander M. G.
Hernandez-Hernandez, Daniel
author_facet Cox, Alexander M. G.
Hernandez-Hernandez, Daniel
contents We consider an agent who has access to a financial market, including derivative contracts, who looks to maximise her utility. Whilst the agent looks to maximise utility over one probability measure, or class of probability measures, she must also ensure that the mark-to-market value of her portfolio remains above a given threshold. When the mark-to-market value is based on a more pessimistic valuation method, such as model-independent bounds, we recover a novel optimisation problem for the agent where the agents investment problem must satisfy a pathwise constraint. For complete markets, the expression of the optimal terminal wealth is given, using the max-plus decomposition for supermartingales. Moreover, for the Black-Scholes-Merton model the explicit form of the process involved in such decomposition is obtained, and we are able to investigate numerically optimal portfolios in the presence of options which are mispriced according to the agent's beliefs.
format Preprint
id arxiv_https___arxiv_org_abs_2512_24371
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Utility Maximisation with Model-independent Constraints
Cox, Alexander M. G.
Hernandez-Hernandez, Daniel
Mathematical Finance
Portfolio Management
Risk Management
We consider an agent who has access to a financial market, including derivative contracts, who looks to maximise her utility. Whilst the agent looks to maximise utility over one probability measure, or class of probability measures, she must also ensure that the mark-to-market value of her portfolio remains above a given threshold. When the mark-to-market value is based on a more pessimistic valuation method, such as model-independent bounds, we recover a novel optimisation problem for the agent where the agents investment problem must satisfy a pathwise constraint. For complete markets, the expression of the optimal terminal wealth is given, using the max-plus decomposition for supermartingales. Moreover, for the Black-Scholes-Merton model the explicit form of the process involved in such decomposition is obtained, and we are able to investigate numerically optimal portfolios in the presence of options which are mispriced according to the agent's beliefs.
title Utility Maximisation with Model-independent Constraints
topic Mathematical Finance
Portfolio Management
Risk Management
url https://arxiv.org/abs/2512.24371