1,195 research outputs found
Multifractal products of stationary diffusion processes
No full textWe investigate the properties of multifractal products of the exponential of stationary diffusion processes defined by stochastic differential equations with linear drift and certain form of the diffusion coefficient corresponding to a variety of marginal distributions. The conditions on the mean, variance and covariance functions of these processes are interpreted in terms of the moment generating functions. We provide three illustrative examples of normal, gamma and beta distributions. We establish the corresponding lognormal, log-gamma and log-beta scenarios for the limiting processes, including their Rényi functions and dependence structure
Multifractality of products of geometric Ornstein-Uhlenbeck -type processes
Get PDFWe investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by Lévy motion. The conditions on the mean, variance, and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We consider five cases of infinitely divisible distributions for the background driving Lévy processes, namely, the gamma and variance gamma distributions, the inverse Gaussian and normal inverse Gaussian distributions, and the z-distributions. We establish the corresponding scenarios for the limiting processes, including their Rényi functions and dependence structure
Simulation of multifractal products of Ornstein-Uhlenbeck type processes
No full textThis paper investigates and provides evidence of the multifractal properties of products of the exponential of Ornstein–Uhlenbeck processes driven by Lévy motion. We demonstrate in detail the construction of a multifractal process with gamma subordinator as the background driving Lévy process. Simulations are performed for the scenarios corresponding to the normal inverse Gaussian, gamma and inverse Gaussian distributions. The log periodograms and Rényi functions of the simulated processes are also computed to investigate their multifractality
Uniqueness result for an age-dependent reaction-diffusion problem
No full textThis paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the presence of, for example, mortality and reaction processes. Our result shows that in a spatial environment, if two population densities obey the same evolution equation and possess the same terminal data of time and age, then their distributions must coincide therein.This work is in commemoration of the first death anniversary of V. A. K's father. V. A. K thanks Prof. Nguyen Huy Tuan for introducing him the ultraparabolic problem. The work of V.A.K. was supported by the Research Foundation-Flanders (FWO) under the project 'Approximations for forward and inverse reaction-diffusion problems related to cancer models'.Lesnic, D (reprint author), Univ Leeds, Dept Appl Math, Leeds, W Yorkshire, England.
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Linear filtering of systems with memory and application to finance
Full text linkWe study the linear filtering problem for systems driven by continuous Gaussian processes V(1) and V(2) with memory described by two parameters. The processes V(j) have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. They allow for straightforward parameter estimations. After giving the semimartingale representations of V(j) by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations
On a pore-scale stationary diffusion equation: Scaling effects and correctors for the homogenization limit
No full textIn this paper, we consider a microscopic semilinear elliptic equation posed in periodically perforated domains and associated with the Fourier-type condition on internal micro-surfaces. The first contribution of this work is the construction of a reliable linearization scheme that allows us, by a suitable choice of scaling arguments and stabilization constants, to prove the weak solvability of the microscopic model. Asymptotic behaviors of the microscopic solution with respect to the microscale parameter are thoroughly investigated in the second theme, based upon several cases of scaling. In particular, the variable scaling illuminates the trivial and non-trivial limits at the macroscale, confirmed by certain rates of convergence. Relying on classical results for homogenization of multiscale elliptic problems, we design a modified two-scale asymptotic expansion to derive the corresponding macroscopic equation, when the scaling choices are compatible. Moreover, we prove the high-order corrector estimates for the homogenization limit in the energy space H-1, using a large amount of energy-like estimates. A numerical example is provided to corroborate the asymptotic analysis.The work of V. A. K was partly supported by the Research Foundation-Flanders (FWO) under the project named "Approximations for forward and inverse reaction-diffusion problems related to cancer models". This work was also supported by US Army Research Laboratory and US Army Research Office grant W911NF-19-1-0044.Khoa, VA (corresponding author), Hasselt Univ, Fac Sci, Campus Diepenbeek, BE-3590 Diepenbeek, Belgium.
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Semiparametric approximation methods in multivariate model selection
No full textIn this paper we propose a cross-validation selection criterion to determine asymptotically the correct model among the family of all possible partially linear models when the underlying model is a partially linear model. We establish the asymptotic consistency of the criterion. In addition, the criterion is illustrated using two real sets of data.Jiti Gao, Rodney Wolff and Vo Anhhttp://www.elsevier.com/wps/find/journaldescription.cws_home/622865/description#descriptio
Financial Markets with Memory I: Dynamic Models
Full text linkThis is the first of two papers in which we consider a stock with price process defined by a stochastic differential equation driven by a process Y(·) different from Brownian motion. The adoption of such a colored noise input is motivated by an analysis of real market data. The process Y(·) is defined by a continuous-time AR(∞)-type equation and may have either short or long memory. We show that the process Y(·) has a good MA(∞)-type representation. The existence of such simultaneous good AR(∞) and MA(∞) representations enables us to apply a new method for the calculation of relevant conditional expectations, whence to obtain various explicit results for problems such as portfolio optimization. The financial market defined by the above stock price process is complete, and if the coefficients are constant, then the prices of European calls and puts are given by the Black-Scholes formulas as in the Black-Scholes model. Unlike the latter, however, the model allows for differences between the historical and implied volatilities. The model includes a special case in which only two additional parameters are introduced to describe the memory of the market, compared with the Black-Scholes model. Analysis based on real market data shows that this simple model with two additional parameters is more realistic in capturing the memory effect of the market, while retaining the simplicity and usefulness of the Black-Scholes model
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