arXiv subjects

Sergio A. Almada Monter

Publications and source records attributed to Sergio A. Almada Monter.

6 recordsLinked to original sources

arXiv2018

Dynamics of observables in rank-based models and performance of functionally generated portfolios

In the seminal work [9], several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment decisions, a concise mathematical description of their dynamics has been missing. We fill this gap in the setting of rank-based models and expect our ideas to extend to other models of large financial markets as well. The results are then used to study the performance of multiplicatively and additively functionally generated portfolios, in particular, over short-term and medium-term horizons.

math.PR↗

arXiv2015

Source detection algorithms for dynamic contaminants based on the analysis of a hydrodynamic limit

In this work we propose and numerically analyze an algorithm for detection of a contaminant source using a dynamic sensor network. The algorithm is motivated using a global probabilistic optimization problem and is based on the analysis of the hydrodynamic limit of a discrete time evolution equation on the lattice under a suitable scaling of time and space. Numerical results illustrating the effectiveness of the algorithm are presented.

math.PR↗

arXiv2015

Scaling Limits and Exit Law for Multiscale Diffusions

In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law of the joint distribution of the exit time and exit location. We apply our results to the first order Langevin equation in a rough potential, studying both fluctuations around the typical behavior and the conditional limiting exit law, conditional on the rare event of going against the underlying deterministic flow.

math.PR↗

arXiv2014

Small Noise Estimates of the Quadratic Covariation between Non-smooth Transformations of Brownian Motion

Given a Brownian Motion $W$, in this paper we study the asymptotic behavior, as $\eps \to 0$, of the quadratic covariation between $f (\eps W)$ and $W$ in the case in which $f$ is not smooth. Among the main features discovered is that the speed of the decay in the case $f \in C^α$ is polynomial in $\eps$ and not exponential as expected. We use a recent representation as a backward- forward Itô integral of $[f (\eps W), W]$ to prove an $\eps$-dependent approximation scheme which is of independent interest. We get the result by providing estimates to this approximation.

math.PR↗

arXiv2014

Infinite Dimensional Forward-Backward Stochastic Differential Equations and the KPZ Equation

Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation(SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of this equation. Bertini, Cancrini and Giacomin have proposed a notion of a solution through a limiting procedure and a certain renormalization of the nonlinearity. In this work we study connections between the KPZ equation and certain infinite dimensional forward-backward stochastic differential equations. Forward-backward equations with a finite dimensional noise have been studied extensively, mainly motivated by problems in mathematical finance. Equations considered here differ from the classical works in that, in addition to having an infinite dimensional driving noise, the associated SPDE involves a non-Lipschitz (namely a quadratic) function of the gradient. Existence and uniqueness of solutions of such infinite dimensional forward-backward equations is established and the terminal values of the solutions are then used to give a new probabilistic representation for the solution of the KPZ equation.

math.PR↗

arXiv2014

Scaling Limit for the Diffusion Exit Problem, a Survey

In this review, an outline of the so called Freidlin-Wentzell theory and its recent extensions is given. Broadly, this theory studies the exponential rate at which the probabilities of rare events related to random perturbation of ODE decays. The typical situation is when an ODE has several stable equilibria, in which case, the theory predicts the most likely paths in which the randomly perturbed system goes from one equilibria to another. In recent developments I will outline how recent approaches allows to distinguish between paths that are otherwise exponentially equivalent and provide an overview of applications of this theory. In particular, we outline the influence of this theory in Monte Carlo Algorithms and Simulated Annealing schemes.

math.PR↗