Related papers: On non-linear dependence of multivariate subordina…
This article deals with adaptive nonparametric estimation for L\'evy processes observed at low frequency. For general linear functionals of the L\'evy measure, we construct kernel estimators, provide upper risk bounds and derive rates of…
In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain…
Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…
In this paper, we develop a method to model and estimate several, _dependent_ count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of…
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…
We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling…
We address an important yet challenging problem - modeling high-dimensional dependencies across multivariates such as financial indicators in heterogeneous markets. In reality, a market couples and influences others over time, and the…
We characterize the small-time asymptotic behavior of the exit probability of a L\'evy process out of a two-sided interval and of the law of its overshoot, conditionally on the terminal value of the process. The asymptotic expansions are…
We develop factor copula models for analysing the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric…
In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
These lectures notes aim at introducing L\'{e}vy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of L\'{e}vy processes. We analyze a `toy' example of a…
In this paper, we study a multivariate gamma subordinator whose components are independent gamma processes subject to a random time governed by an independent negative binomial process. We derive the explicit expressions for its joint…
The thesis is composed of three parts. Part I introduces the mathematical and statistical tools that are relevant for the study of dependences, as well as statistical tests of Goodness-of-fit for empirical probability distributions. I…
Multivariate processes with long-range dependence properties can be encountered in many fields of application. Two fundamental characteristics in such frameworks are long-range dependence parameters and correlations between component time…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
We extend generalized functional linear models under independence to a situation in which a functional covariate is related to a scalar response variable that exhibits spatial dependence-a complex yet prevalent phenomenon. For estimation,…
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences…
This brief manuscript provides an introduction to L\'evy processes and their applications in finance as the random process that drives asset models. Characteristic functions and random variable generators of popular L\'evy processes are…
Assessing dependence within co-movements of financial instruments has been of much interest in risk management. Typically, indices of tail dependence are used to quantify the strength of such dependence, although many of the indices…