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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50206 - Finance

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Risks

ISSN

2227-9091

e-ISSN

—

Svazek periodika

13

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

27

Strana od-do

1-27

Kód UT WoS článku

001474605600001

EID výsledku v databázi Scopus

2-s2.0-105003456839