1,151 research outputs found
Matrix geometric approach for random walks: stability condition and equilibrium distribution
In this paper, we analyse a sub-class of two-dimensional homogeneous nearest
neighbour (simple) random walk restricted on the lattice using the matrix
geometric approach. In particular, we first present an alternative approach for
the calculation of the stability condition, extending the result of Neuts drift
conditions [30] and connecting it with the result of Fayolle et al. which is
based on Lyapunov functions [13]. Furthermore, we consider the sub-class of
random walks with equilibrium distributions given as series of product-forms
and, for this class of random walks, we calculate the eigenvalues and the
corresponding eigenvectors of the infinite matrix appearing in the
matrix geometric approach. This result is obtained by connecting and extending
three existing approaches available for such an analysis: the matrix geometric
approach, the compensation approach and the boundary value problem method. In
this paper, we also present the spectral properties of the infinite matrix
The least squares method for option pricing revisited
It is shown that the the popular least squares method of option pricing
converges even under very general assumptions. This substantially increases the
freedom of creating different implementations of the method, with varying
levels of computational complexity and flexible approach to regression. It is
also argued that in many practical applications even modest non-linear
extensions of standard regression may produce satisfactory results. This claim
is illustrated with examples
Spatial Smoothing Techniques for the Assessment of Habitat Suitability
Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of the observations is often violated in practice since the points at which the observations are collected are spatially aligned. While several approaches have been developed to analyse and account for spatial correlation in regression models with normally distributed responses, far less work has been done in the context of generalised linear models. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations
Pricing Ratchet equity-indexed annuities with early surrender risk in a CIR++ model
International audienceIn connection with a problem posed by Kijima and Wong \cite{kw}, we propose a lattice algorithm for pricing simple Ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR++ stochastic interest rates. In addition we present an asymptotic expansion technique which permits to obtain a first order approximation formula for the price of simple Ratchet EIAs without early surrender risk and without global minimum contract value. Numerical comparisons show the reliability of the proposed methods.Suite au problème posé par Kijima et Wong, nous proposons un algorithme de treillis pour le pricing du Ratchet sur action avec risque de rachat anticipé. Il inclut aussi une valeur minimale globale lorsque l'actif dépend du processus CIR++ du taux d'intérêt. Par ailleurs, nous présentons une technique de développement asymptotique permettant une approximation de premier ordre pour le prix du Ratchet EIAs, sans risque de rachat anticipé ni valeur minimale. Des expériences numériques montrent une bonne qualité des résultats obtenus par la méthode proposée
A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure
A new unified modelling framework based on the superposition of additive submodels, functional components, and
wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented
using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown
analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear
autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional
component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and
multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters
problem, which can be solved using least-squares type methods. An efficient model structure determination
approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization
of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is
employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to
as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to
represent high-order and high dimensional non-linear systems
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