Related papers: A selective overview of nonparametric methods in f…
Diffusion models play an essential role in modeling continuous-time stochastic processes in the financial field. Therefore, several proposals have been developed in the last decades to test the specification of stochastic differential…
One of the most important empirical findings in microeconometrics is the pervasiveness of heterogeneity in economic behaviour (cf. Heckman 2001). This paper shows that cumulative distribution functions and quantiles of the nonparametric…
We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…
Literature highlighted that financial time series data pose significant challenges for accurate stock price prediction, because these data are characterized by noise and susceptibility to news; traditional statistical methodologies made…
Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…
In this paper we consider nonparametric estimation for dependent data, where the observations do not necessarily come from a linear process. We study density estimation and also discuss associated problems in nonparametric regression using…
In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…
Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that…
We develop new econometric methods for the comparison of nonparametric time trends. In many applications, practitioners are interested in whether the observed time series all have the same time trend. Moreover, they would often like to know…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion…
We introduce a \textit{non-modal} analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems. While strictly speaking only valid for linear problems, the analysis is…
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
This paper presents a pre-processing and a distance which improve the performance of machine learning algorithms working on independent and identically distributed stochastic processes. We introduce a novel non-parametric approach to…
Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…