Minimal Entropy and Entropic Risk Measures: A Unified Framework via Relative Entropy

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F04274644%3A_____%2F25%3A%230001219" target="_blank" >RIV/04274644:_____/25:#0001219 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.3390/risks13040070" target="_blank" >https://doi.org/10.3390/risks13040070</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/risks13040070" target="_blank" >10.3390/risks13040070</a>

Result language

angličtina

Original language name

Minimal Entropy and Entropic Risk Measures: A Unified Framework via Relative Entropy

Original language description

We introduce a new coherent risk measure, the minimal-entropy risk measure, which is built on the minimal-entropy σ-martingale measure—a concept inspired by the well-known minimal-entropy martingale measure used in option pricing. While the minimal-entropy martingale measure is commonly used for pricing and hedging, the minimal-entropy σ-martingale measure has not previously been studied, nor has it been analyzed as a traditional risk measure. We address this gap by clearly defining this new risk measure and examining its fundamental properties. In addition, we revisit the entropic risk measure, typically expressed through an exponential formula. We provide an alternative definition using a supremum over Kullback–Leibler divergences, making its connection to entropy clearer. We verify important properties of both risk measures, such as convexity and coherence, and extend these concepts to dynamic situations. We also illustrate their behavior in scenarios involving optimal risk transfer. Our results link entropic concepts with incomplete-market pricing and demonstrate how both risk measures share a unified entropy-based foundation.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

50206 - Finance

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Risks

ISSN

2227-9091

e-ISSN

—

Volume of the periodical

13

Issue of the periodical within the volume

4

Country of publishing house

CH - SWITZERLAND

Number of pages

27

Pages from-to

1-27

UT code for WoS article

001474605600001

EID of the result in the Scopus database

2-s2.0-105003456839