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Thierry Jeulin

Bio: Thierry Jeulin is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 369 citations.

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Book
01 Jan 1979
TL;DR: In this paper, the second volume follows on from the first, concentrating on stochastic integrals, stochy differential equations, excursion theory and the general theory of processes.
Abstract: This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

1,804 citations

Journal ArticleDOI
Abstract: We define three types of non causal stochastic integrals: forward, backward and symmetric. Our approach consists in approximating the integrator. Two optics are considered: the first one is based on traditional usual stochastic calculus and the second one on Wiener distributions.

366 citations

Journal ArticleDOI
TL;DR: In this article, the first hitting times of squared Bessel processes and radial Ornstein-Uhlenbeck processes with negative dimensions or negative starting points are studied. But the authors focus on the first time a Bessel process hits a given barrier.
Abstract: Bessel processes play an important role in financial mathematics because of their strong relation to financial models such as geometric Brownian motion or Cox-Ingersoll-Ross processes. We are interested in the first time Bessel processes and, more generally, radial Ornstein-Uhlenbeck processes hit a given barrier. We give explicit expressions of the Laplace transforms of first hitting times by (squared) radial Ornstein-Uhlenbeck processes, that is, Cox-Ingersoll-Ross processes. As a natural extension we study squared Bessel processes and squared Ornstein-Uhlenbeck processes with negative dimensions or negative starting points and derive their properties.

336 citations

Journal ArticleDOI
TL;DR: In this paper, a stochastic control problem arising in financial economics is studied to maximize expected logarithmic utility from terminal wealth and/or consumption, where the portfoilo is allowed to anticipate the future, i.e. the terminal values of the prices or of the driving Brownian motion.
Abstract: We study a classical stochastic control problem arising in financial economics: to maximize expected logarithmic utility from terminal wealth and/or consumption. The novel feature of our work is that the portfoilo is allowed to anticipate the future, i.e. the terminal values of the prices, or of the driving Brownian motion, are known to the investor, either exactly or with some uncertainty. Results on the finiteness of the value of the control problem are obtained in various setups, using techniques from the so-called enlargement of filtrations. When the value of the problem is finite, we compute it explicitly and exhibit an optimal portfolio in closed form.

225 citations