The General Semimartingale Market Model

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

The General Semimartingale Market Model

Original language description

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.

Czech name

—

Czech description

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Type

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

CEP classification

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OECD FORD branch

50200 - Economics and Business

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

AppliedMath

ISSN

2673-9909

e-ISSN

—

Volume of the periodical

5

Issue of the periodical within the volume

3

Country of publishing house

CH - SWITZERLAND

Number of pages

28

Pages from-to

1-28

UT code for WoS article

001579412100001

EID of the result in the Scopus database

2-s2.0-105017455864