arXiv subjects

Massinissa Ferhoune

Publications and source records attributed to Massinissa Ferhoune.

4 recordsLinked to original sources

arXiv2025

Nonconcave Robust Utility Maximization under Projective Determinacy

We study a general robust utility maximization problem in a discrete-time frictionless market. The investor is assumed to have a possibly infinite, random, nonconcave, and nondecreasing utility function defined on the whole real line. She also faces model ambiguity on her beliefs about the market, which is modelled through a set of priors. We assume that the utility and the prices are projective functions of the path, while the graphs of the local priors are projective sets. Our other assumptions are stated on a prior-by-prior basis and correspond to generally accepted assumptions in the literature on markets without ambiguity. Under the set-theoretic axiom of Projective Determinacy (PD), our main result is the existence of an optimal investment strategy when the utility function is also upper-semicontinuous. We further provide several counterexamples justifying our assumptions.

q-fin.MF↗

arXiv2025

Projective functions

We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums, differences, products, finite suprema and infima, sections and compositions. Assuming the set-theoretical axiom of Projective Determinacy, we also prove measurable selection results, stability under integration, and the existence of $ε$-optimal selectors. Finally, we illustrate how these results are important in the context of model uncertainty.

math.LO↗

arXiv2024

Discrete time optimal investment under model uncertainty

We study a robust utility maximization problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real-line. She also faces model ambiguity on her beliefs about the market, which is modeled through a set of priors. We prove the existence of an optimal investment strategy using only primal methods. For that we assume classical assumptions on the market and on the random utility function as asymptotic elasticity constraints. Most of our other assumptions are stated on a prior-by-prior basis and correspond to generally accepted assumptions in the literature on markets without ambiguity. We also propose a general setting including utility functions with benchmark for which our assumptions are easily checked.

q-fin.MF↗

arXiv2024

Efficient approximations for utility-based pricing

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.

q-fin.CP↗