A diffusion can be thought of as a strong Markov process (in ℝ n ) with continuous paths. Before
the development of Itô’s theory of stochastic integration for Brownian motion, the primary …

This paper studies asset price bubbles in a continuous time model using the local martingale
framework. Providing careful definitions of the asset's market and fundamental price, we …

We have made small changes throughout the book, including the exercises, and we have
tried to correct if not all, then at least most of the typos. We wish to thank the many colleagues …

Recently, various authors proposed Monte-Carlo methods for the computation of American
option prices, based on least squares regression. The purpose of this paper is to analyze an …

Over the last 10 years or so a mathematical theory of bubbles has emerged, in the spirit of a
martingale theory based on an absence of arbitrage, as opposed to an equilibrium theory. …

In this paper we investigate the nature of the adapted solutions to a class of forward-backward
stochastic differential equations (SDEs for short) in which the forward equation is non-…

Assuming that {(X n ,Y n )} is a sequence of cadlag processes converging in distribution to (X,Y)
in the Skorohod topology, conditions are given under which the sequence {∫ X n dY n } …

Classical theories of financial markets assume an infinitely liquid market and that all traders
act as price takers. This theory is a good approximation for highly liquid stocks, although …

We are interested in the rate of convergence of the Euler scheme approximation of the
solution to a stochastic differential equation driven by a general (possibly discontinuous) …

For about ten years, models of stochastic particle systems with mean field interaction have
been studied in detail, about their asymptotic behaviour when the size of the system becomes …