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...

Many investors do not know with certainty when their portfolio will be liquidated. Should their portfolio selection be influenced by the uncertainty of exit time? In order to answer this question, we consider a suitable extension of the familiar optimal investment problem of Merton [Merton,...

We provide a concise exposition of theoretical results that appear in modeling default time as a random time, we study in details the invariance martingale property and we establish a representation theorem which leads, in a complete market setting, to the hedging portfolio of a vulnerable...

This paper is the first in a series that we devote to studying the problems of valuation and hedging of defaultable game options in general, and convertible corporate bonds in particular. Here, we present mathematical foundations for our overall study. Specifically, we provide several results...

This paper studies in some examples the role of information in a default-risk framework. We examine three types of information for a firm's unlevered asset value to the secondary bond market: the classical case of continuous and perfect information, observation of past and contemporaneous asset...

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time $\tau$. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model...

We apply the default density framework developed in El Karoui et al. \cite{ejj1} to modelling of multiple defaults, which can be adapted to both top-down and bottom-up models. We present general pricing results and establish links with the classical intensity approach. Explicit models are also...