P-Sensitive Functions and Localizations

TL;DR

This paper develops a theory of P-sensitive functions within a robust stochastic framework, providing representations via localization and applying these to optimization, risk measures, and financial models.

Contribution

It introduces the concept of P-sensitive functions, characterizes them through localization, and applies this to robust optimization and financial no-arbitrage analysis.

Findings

P-sensitive functions are characterized by functional localization.

The framework applies to robust optimization problems.

Insights into convex risk measures and no-arbitrage conditions.

Abstract

This paper assumes a robust stochastic model where a set $\mathcal{P}$ of probability measures replaces the single probability measure of dominated models. We introduce and study $\mathcal{P}$-sensitive functions defined on robust function spaces of random variables. We show that $\mathcal{P}$-sensitive functions are precisely those that admit a representation via so-called functional localization. The theory is applied to solving robust optimization problems, to convex risk measures, and to the study of no arbitrage in robust one-period financial models.