In the last forty years, the theory of financial markets has become a growing field of interest for academics as well as for practitioners. We present here an overview of the main topics.

This book explains key financial concepts, mathematical tools and theories of mathematical finance. It is organized in four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets...

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time τ gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit...

An asset is considered whose logarithmic price is the sum of a drift term, a Brownian motion and jumps of a Poisson process. Various items of future information about the price process are considered available to an informed agent. The optimal attainable wealths of both informed and uninformed...

An asset is considered whose logarithmic price is the sum of a drift term, a Brownian motion and jumps of a Poisson process. Various items of future information about the price process are considered available to an informed agent. The optimal attainable wealths of both informed and uninformed...

This paper completes the two studies undertaken in \cite{aksamit/choulli/deng/jeanblanc2} and \cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called NUPBR hereafter) when the stock price...

We consider a financial market with a savings account and a stock S that follows a general diffusion. The default of the company, which issues the stock S, is modeled as a stopping time with respect to the filtration generated by the value of the firm that is not observable by regular investors....