Enlargement of filtration with finance in view

A Aksamit, M Jeanblanc - 2017 - Springer
At the end of the 1970s, Jean Jacod, Thierry Jeulin and Marc Yor started a systematic study
of enlargement of filtration which focuses on the properties of stochastic processes under a …

Generalized BSDE and reflected BSDE with random time horizon

A Aksamit, L Li, M Rutkowski - Electronic Journal of Probability, 2023 - projecteuclid.org
Motivated by structural, reduced-form and hybrid models of the third party and counterparty
credit risk, we study a generalized backward stochastic differential equations (BSDE) up to a …

No-arbitrage up to random horizon for quasi-left-continuous models

A Aksamit, T Choulli, J Deng, M Jeanblanc - Finance and Stochastics, 2017 - Springer
This paper studies the impact, on no-arbitrage conditions, of stopping the price process at an
arbitrary random time. As price processes, we consider the class of quasi-left-continuous …

[HTML][HTML] The strong predictable representation property in initially enlarged filtrations under the density hypothesis

C Fontana - Stochastic Processes and their Applications, 2018 - Elsevier
We study the strong predictable representation property in filtrations initially enlarged with a
random variable L. We prove that the strong predictable representation property can always …

A martingale representation theorem and valuation of defaultable securities

T Choulli, C Daveloose, M Vanmaele - Mathematical finance, 2020 - Wiley Online Library
We consider a financial framework with two levels of information: the public information
generated by the financial assets, and a larger flow of information that contains additional …

No-arbitrage for informational discrete time market models

T Choulli, J Deng - Stochastics, 2017 - Taylor & Francis
This paper focuses on the stability of no-arbitrage, for discrete time market models, under
additional uncertainty generated by a random time. At the practical level, this random time …

No-arbitrage under a class of honest times

A Aksamit, T Choulli, J Deng, M Jeanblanc - Finance and Stochastics, 2018 - Springer
This paper quantifies the interplay between the no-arbitrage notion of no unbounded profit
with bounded risk (NUPBR) and additional progressive information generated by a random …

Log-optimal and numéraire portfolios for market models stopped at a random time

T Choulli, S Yansori - Finance and Stochastics, 2022 - Springer
This paper focuses on numéraire and log-optimal portfolios when a market model (S, F, P)–
specified by its assets' price S, its flow of information F and a probability measure P–is …

Vulnerable European and American options in a market model with optional hazard process

L Li, R Liu, M Rutkowski - arXiv preprint arXiv:2212.12860, 2022 - arxiv.org
We study the upper and lower bounds for prices of European and American style options
with the possibility of an external termination, meaning that the contract may be terminated at …

Arbitrage and utility maximization in market models with an insider

HN Chau, WJ Runggaldier, P Tankov - Mathematics and Financial …, 2018 - Springer
We study arbitrage opportunities, market viability and utility maximization in market models
with an insider. Assuming that an economic agent possesses an additional information in …