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Continuous martingales and Brownian motion
0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.-
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
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
Mathematical Methods for Financial Markets
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
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
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
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
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
Exponential functionals of Levy processes
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