σ-Martingales: Foundations, Properties, and a New Proof of the Ansel-Stricker Lemma

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F04274644%3A_____%2F25%3A%230001211" target="_blank" >RIV/04274644:_____/25:#0001211 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/math13040682" target="_blank" >https://doi.org/10.3390/math13040682</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math13040682" target="_blank" >10.3390/math13040682</a>

Jazyk výsledku

angličtina

Název v původním jazyce

σ-Martingales: Foundations, Properties, and a New Proof of the Ansel-Stricker Lemma

Popis výsledku v původním jazyce

σ-martingales generalize local martingales through localizing sequences of predictable sets, which are essential in stochastic analysis and financial mathematics, particularly for arbitrage-free markets and portfolio theory. In this work, we present a new approach to σ-martingales that avoids using semimartingale characteristics. We develop all fundamental properties, provide illustrative examples, and establish the core structure of σ-martingales in a new, straightforward manner. This approach culminates in a new proof of the Ansel–Stricker lemma, which states that one-sided bounded σ-martingales are local martingales. This result, referenced in nearly every publication on mathematical finance, traditionally relies on the original French-language proof. We use this result to prove a generalization, which is essential for defining the general semimartingale model in mathematical finance.

Název v anglickém jazyce

σ-Martingales: Foundations, Properties, and a New Proof of the Ansel-Stricker Lemma

Popis výsledku anglicky

σ-martingales generalize local martingales through localizing sequences of predictable sets, which are essential in stochastic analysis and financial mathematics, particularly for arbitrage-free markets and portfolio theory. In this work, we present a new approach to σ-martingales that avoids using semimartingale characteristics. We develop all fundamental properties, provide illustrative examples, and establish the core structure of σ-martingales in a new, straightforward manner. This approach culminates in a new proof of the Ansel–Stricker lemma, which states that one-sided bounded σ-martingales are local martingales. This result, referenced in nearly every publication on mathematical finance, traditionally relies on the original French-language proof. We use this result to prove a generalization, which is essential for defining the general semimartingale model in mathematical finance.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

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

Mathematics

ISSN

2227-7390

e-ISSN

—

Svazek periodika

13

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

19

Strana od-do

1-19

Kód UT WoS článku

001430337600001

EID výsledku v databázi Scopus

2-s2.0-85218978045