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Continuous martingales and Brownian motion

- Daniel Revuz, M. Yor
- Mathematics
- 1990

0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.-… Expand

The fine structure of asset returns: an empirical investigation

We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and… Expand

The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator

The two-parameter Poisson-Dirichlet distribution, denoted PD(α,θ), is a probability distribution on the set of decreasing positive sequences with sum 1. The usual Poisson-Dirichlet distribution with… Expand

Mathematical Methods for Financial Markets

- M. Jeanblanc, M. Yor, M. Chesney
- Mathematics
- 23 November 2009

Stochastic processes of common use in mathematical finance are presented throughout this book, which consists of eleven chapters, interlacing on the one hand financial concepts and instruments, such… Expand

Stochastic Volatility for Lévy Processes

Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean‐reverting square root process. The… Expand

BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES

Using Bessel processes, one can solve several open problems involving the integral of an exponential of Brownian motion. This point will be illustrated with three examples. The first one is a formula… Expand

On Some Exponential Functionals of Brownian Motion

- M. Yor
- Mathematics
- 1 September 1992

In this paper, distributional questions which arise in certain mathematical finance models are studied: the distribution of the integral over a fixed time interval [0, T]of the exponential of… Expand

Stochastic Volatility for Levy Processes

Three processes reflecting persistence of volatility are formulated by evaluating three Levy processes at a time change given by the integral of a square root process. A positive stock price process… Expand

Exponential functionals of Levy processes

- J. Bertoin, M. Yor
- Mathematics
- 1 November 2005

The distribution of the terminal value A∞ of the exponential functional
$$ {A_t}(\xi ) = \smallint _0^t{e^{{\xi _s}}}ds $$
of a Levy process (ξ t ) t≥0 plays an important role in Mathematical… Expand

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