2024/03/18 by Laurence Carassus, Carassus, Laurence, Massinissa Ferhoune +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #28B20 #54H05 #60A10 #91B16 #91G80 #93E20 #Decision-Making and Behavioral Economics #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2403.11824
openalex publication_date 2024/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.