Optimal Portfolio

Utility Maximisation with Model-independent Constraints ArXiv ID: 2512.24371 “View on arXiv” Authors: Alexander M. G. Cox, Daniel Hernandez-Hernandez Abstract 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. ...

Exponential Utility Maximization in a Discrete Time Gaussian Framework ArXiv ID: 2305.18136 “View on arXiv” Authors: Unknown Abstract The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in Mathematical Finance, we also consider an investor who is informed about the risky asset’s price changes with a delay. Our method of solution is based on the theory developed in [“4”] and guessing the optimal portfolio. ...