Common Mathematical Foundations of Expected Utility and Dual Utility Theories

We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new integral representations of dual utility models

Schwinger-Dyson approach to Liouville Field Theory

We discuss Liouville field theory in the framework of Schwinger-Dyson approach and derive a functional equation for the three-point structure constant. We argue the existence of a second Schwinger-Dyson equation on the basis of the duality between the screening charge operators and obtain a second functional equation for the structure constant. We discuss the utility of the two functional equations to fix the structure constant uniquely

A New Example of a Closed Form Mean-Variance Representation

In most finance papers and textbooks mean-variance preferences are usually introduced and motivated as a special case of expected utility theory. In general, the two sufficient conditions to allow this are either quadratic preferences with an arbitrary distribution of stochastic assets, or arbitrary preferences with Normally distributed assets. In the first case, the specific functional form of mean-variance preferences follows naturally. In the second case, the only specific functional form usually provided is the case of negative exponential preferences. In this note, the specific functional form for mean-variance preferences is derived for the much more realistic example of lognormally distributed assets, and constant relative risk aversion (CRRA) preferences.Mean-variance preferences; expected utility; lognormal assets; risk aversion

Representations for optimal stopping under dynamic monetary utility functionals

In this paper we consider the optimal stopping problem for general dynamic monetary utility functionals. Sufficient conditions for the Bellman principle and the existence of optimal stopping times are provided. Particular attention is payed to representations which allow for a numerical treatment in real situations. To this aim, generalizations of standard evaluation methods like policy iteration, dual and consumption based approaches are developed in the context of general dynamic monetary utility functionals. As a result, it turns out that the possibility of a particular generalization depends on specific properties of the utility functional under consideration.monetary utility functionals, optimal stopping, duality, policy iteration

Robust Optimal Control for a Consumption-investment Problem

We give an explicit PDE characterization for the solution of the problem of maximizing the utility of both terminal wealth and intertemporal consumption under model uncertainty. The underlying market model consists of a risky asset, whose volatility and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in terms of a HARA utility function with risk aversion parameter 0Optimal Consumption, Robust Control, Model Uncertainty, Incomplete Markets, Stochastic Volatility, Coherent Risk Measures, Convex Duality