arXiv subjects

Christophe Profeta

Publications and source records attributed to Christophe Profeta.

22 records · Page 2Linked to original sources

arXiv2013

Some limiting laws associated with the integrated Brownian motion

We study some limit theorems for the normalized law of integrated Brownian motion perturbed by several examples of functionals: the first passage time, the nth passage time, the last passage time up to a finite horizon and the supremum. We show that the penalization principle holds in all these cases and give descriptions of the conditioned processes. In particular, it is remarkable that the penalization by the nth passage time is independent of n, and always gives the same conditioned process, i.e. integrated Brownian motion conditioned not to hit 0. Our results rely on some explicit formulae obtained by Lachal and on enlargement of filtrations.

math.PR↗

arXiv2012

On last passage times of linear diffusions to curved boundaries

The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following Robbins & Siegmund, we then show that this expression may be computed for some implicit boundaries via a martingale method. Finally, we discuss some links between first hitting times and last passage times via time inversion, and present an integral equation (which we solve in some particular cases) satisfied by the density of the last passage time. Many examples are given in the Brownian and Bessel frameworks.

math.PR↗

arXiv2011

Penalizing null recurrent diffusions

We present some limit theorems for the normalized laws (with respect to functionals involving last passage times at a given level up to time t) of a large class of null recurrent diffusions. Our results rely on hypotheses on the Lévy measure of the diffusion inverse local time at 0. As a special case, we recover some of the penalization results obtained by Najnudel, Roynette and Yor in the (reflected) Brownian setting.

math.PR↗

arXiv2009

Mathematical model for resistance and optimal strategy

We propose a mathematical model for one pattern of charts studied in technical analysis: in a phase of consolidation, the price of a risky asset goes down $ξ$ times after hitting a resistance level. We construct a mathematical strategy and we calculate the expectation of the wealth for the logaritmic utility function. Via simulations, we compare the strategy with the standard one.

math.PR↗