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...

The purpose of this paper is to study the immersion property within a credit risk modeling. The construction of a credit model by enlargement of a reference Filtration with the progressive knowledge of a credit event has become a standard for reduced form modeling. It is known that such a...

The preservation of the semi-martingale property in a progressive enlargement of filtration has been studied by many authors. Most of them focus on progressive enlargement with a honest time, allowing for semi-martingale invariance and simple decomposition formulas. However, times allowing for...

In some examples, we study the role of information in a default-risky framework. The analysis is based on the assumption that the investors in defaultable bonds obtain information about the firm's unlevered asset value at discrete dates. The discrete information arrivals induce...

In this paper we consider the optimization problem of an agent who wants to maximize the total expected discounted utility from consumption over an infinite horizon. The agent is under obligation to pay a debt at a fixed rate until he/she declares bankruptcy. At that point, after paying a fixed...

We first discuss some mathematical tools used to compute the intensity of a single jump process, in its canonical filtration. In the second part, we try to clarify the meaning of default and the links between the default time, the asset?s filtration, and the intensity of the default time. We...

We present the solution of a portfolio optimization problem for an economic agent endowed with a stochastic insurable stream, under a liquidity constraint over the time interval [0,T]. Generally, the existence of labor income complicates the agent's decisions. Moreover, in the real world the...