Consider an equity market with $n$ stocks. The vector of proportions of the total market capitalizations that belongs to each stock is called the market weight. The market weight defines a buy-and-hold portfolio called the market portfolio whose value represents the performance of the entire...

We introduce a framework to analyze the relative performance of a portfolio with respect to a benchmark market index. We show that this relative performance has three components: a term that can be interpreted as energy coming from the market fluctuations, a relative entropy term that measures...

We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them with the collections of ordered processes in a Brownian...

We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict...

Department: Statistics.

Consider an agent who enters a financial market on day t = 0 with an initial capital amount x. He invests this amount on stocks and the money market, and by day t = T, has generated a wealth W . He is given a convex class of probability measures (called scenarios) and a real-valued function (or...

We consider a trader who wants to direct his portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a black-box algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and whose outputs are the numerical values of initial capital...

We study strict local martingales via h-transforms, a method which first appeared in work by Delbaen and Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old...