Data-driven nonlinear expectations for statistical uncertainty in decisions

TL;DR

This paper explores how to explicitly incorporate statistical uncertainty in decision-making by using nonlinear expectations to model the uncertainty in estimating probability measures.

Contribution

It introduces a framework for integrating statistical uncertainty into decision valuation through the theory of nonlinear expectations.

Findings

Provides a consistent method for modeling uncertainty in probability estimates.

Demonstrates the application of nonlinear expectations in decision problems.

Enhances decision robustness by accounting for estimation errors.

Abstract

In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be explicitly and consistently incorporated in the valuation of decisions, using the theory of nonlinear expectations.