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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
σ-Martingales: Foundations, Properties, and a New Proof of the Ansel-Stricker Lemma
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics

Project
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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

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