The General Semimartingale Market Model

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F04274644%3A_____%2F25%3A%230001255" target="_blank" >RIV/04274644:_____/25:#0001255 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/appliedmath5030097" target="_blank" >https://doi.org/10.3390/appliedmath5030097</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/appliedmath5030097" target="_blank" >10.3390/appliedmath5030097</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The General Semimartingale Market Model

Popis výsledku v původním jazyce

This paper develops a unified framework for mathematical finance under general semimartingale models that allow for dividend payments, negative asset prices, and unbounded jumps. We present a rigorous approach to the mathematical modeling of financial markets with dividend-paying assets by defining appropriate concepts of numéraires, discounted processes, and self-financing trading strategies. While most of the mathematical results are not new, this unified framework has been missing in the literature. We carefully examine the transition between nominal and discounted price processes and define appropriate notions of admissible strategies that work naturally in both settings. By establishing the equivalence between these models and providing clear conditions for their applicability, we create a mathematical foundation that encompasses a wide range of realistic market scenarios and can serve as a basis for future work on mathematical finance and derivative pricing. We demonstrate the practical relevance of our framework through a comprehensive application to dividend-paying equity markets where the framework naturally handles discrete dividend payments. This application shows that our theoretical framework is not merely abstract but provides the rigorous foundation for pricing derivatives in real-world markets where classical assumptions need extension.

Název v anglickém jazyce

The General Semimartingale Market Model

Popis výsledku anglicky

This paper develops a unified framework for mathematical finance under general semimartingale models that allow for dividend payments, negative asset prices, and unbounded jumps. We present a rigorous approach to the mathematical modeling of financial markets with dividend-paying assets by defining appropriate concepts of numéraires, discounted processes, and self-financing trading strategies. While most of the mathematical results are not new, this unified framework has been missing in the literature. We carefully examine the transition between nominal and discounted price processes and define appropriate notions of admissible strategies that work naturally in both settings. By establishing the equivalence between these models and providing clear conditions for their applicability, we create a mathematical foundation that encompasses a wide range of realistic market scenarios and can serve as a basis for future work on mathematical finance and derivative pricing. We demonstrate the practical relevance of our framework through a comprehensive application to dividend-paying equity markets where the framework naturally handles discrete dividend payments. This application shows that our theoretical framework is not merely abstract but provides the rigorous foundation for pricing derivatives in real-world markets where classical assumptions need extension.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50200 - Economics and Business

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

AppliedMath

ISSN

2673-9909

e-ISSN

—

Svazek periodika

5

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

28

Strana od-do

1-28

Kód UT WoS článku

001579412100001

EID výsledku v databázi Scopus

2-s2.0-105017455864