Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows

TL;DR

This paper extends the stochastic flow approach to construct a broad class of consistent utility processes with a specified optimal portfolio, using minimal assumptions and convex constraints.

Contribution

It generalizes previous work by defining utilities from a wide class of processes and constructing them via stochastic flows, accommodating convex constraints and minimal assumptions.

Findings

Constructed all consistent utilities with a given optimal process.

Used stochastic flows of homeomorphisms for utility construction.

Proved utility processes are strictly increasing in initial conditions.

Abstract

The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making minimal assumptions and convex constraints on test-processes, we construct by composing two stochastic flows of homeomorphisms, all the consistent stochastic utilities whose the optimal-benchmark process is given, strictly increasing in its initial condition. Proofs are essentially based on stochastic change of variables techniques.