Recover Dynamic Utility from Monotonic Characteristic/Extremal Processes. *

Nicole El Karoui (1) , Mrad Mohamed (2)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
2 LAGA - Laboratoire Analyse, Géométrie et Applications

In the present paper, we are interested in the forward-looking inverse problem, where the observable are a so-called characteristic process $X^c$ and an initial utility function $U (0, .) = u(.)$. The recovery process is a dynamic (eventually random) utility performance $U$. The main result is a necessary and sufficient condition for the existence of a utility performance process $U$ satisfying $U (t, X^c_t (x))$ is a martingale for any initial starting point $x$. Examples of applications are developed in the last section to support our approach in the special case of finance and economics: the first example concerns an aggregation problem, the second one a Markov equilibrium.

Domaines: Finance quantitative [q-fin.CP]; Finance [q-fin.GN]; Gestion de portefeuilles [q-fin.PM]

Nicole El Karoui, Mrad Mohamed. Recover Dynamic Utility from Monotonic Characteristic/Extremal Processes. *. 2018. ⟨hal-01966312v1⟩