Quasiconvex risk measures with markets volatility

TL;DR

This paper explores quasiconvex risk measures in financial markets with volatility, focusing on their properties in variable exponent spaces and providing dual representations to better understand their behavior.

Contribution

It introduces quasiconvex risk measures on variable exponent spaces $L^{p(ullet)}$, extending the theory beyond traditional fixed-exponent spaces and offering dual representation results.

Findings

Extended quasiconvex risk measures to variable exponent spaces

Provided dual representation formulas for these measures

Enhanced understanding of risk in volatile financial markets

Abstract

Since the quasiconvex risk measures is a bigger class than the well known convex risk measures, the study of quasiconvex risk measures makes sense especially in the financial markets with volatility. In this paper, we will study the quasiconvex risk measures defined on a special space $L^{p(\cdot)}$ where the variable exponent $p(\cdot)$ is no longer a given real number like the space $L^{p}$, but a random variable, which reflects the possible volatility of the financial markets. The dual representation for this quasiconvex risk measures will also provided.