A risk measurement approach from risk-averse stochastic optimization of score functions

TL;DR

This paper introduces a novel risk measurement framework for risk-averse stochastic optimization, connecting it with linear regression, deviation measures, and hedging strategies, ensuring solution existence and exploring key properties.

Contribution

It develops a new risk measure based on argmin and minimum concepts, linking stochastic optimization with regression and hedging, and guarantees solution existence.

Findings

Established properties of the argmin as a risk measure

Connected minimum deviation to linear regression models

Linked optimal hedging strategies to the proposed framework

Abstract

We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution. We characterize and explore the properties of the argmin as a risk measure and the minimum as a deviation measure. We provide a connection between linear regression models and our framework. Based on this conception, we consider conditional risk and provide a connection between the minimum deviation portfolio and linear regression. Moreover, we also link the optimal replication hedging to our framework.