Applied Stochastic Models and Data Analysis 

About: Applied Stochastic Models and Data Analysis is an academic journal. The journal publishes majorly in the area(s): Markov process & Stochastic modelling. It has an ISSN identifier of 1099-0747. Over the lifetime, 321 publications have been published receiving 3585 citations.

Multifractal analysis of foreign exchange data

Abstract: In this paper we perform multifractal analyses of five daily Foreign Exchange (FX) rates. These techniques are currently used in turbulence to characterize scaling and intermittency. We show the multifractal nature of FX returns, and estimate the three parameters in the universal multifactal framework, which characterize all small and medium intensity fluctuations, at all scales. For large fluctuations, we address the question of hyperbolic (fat) tails of the distributions which are characterized by a fourth parameter, the tail index. We studied both the prices fluctuations and the returns, finding no systematic difference in the scaling exponents in the two cases. We discuss and compare our results with several recent studies, and show how the additive models are not compatible with data: Brownian, fractional Brownian, Levy, Truncated Levy and fractional Levy models. We analyse in this framework the ARCH(1), GARCH(1,1) and HARCH (7) models, and show that their structure functions scaling exponents are undistinguishable from that of Brownian motion, which means that these models do not adequately describe the scaling properties of the statistics of the data. Our results indicate that there might exist a multiplicative ‘flux of financial information’, which conditions small-scale statistics to large-scale values, as an analogy with the energy flux in turbulence. Copyright © 1999 John Wiley & Sons, Ltd.

Convergence of discretized stochastic (interest rate) processes with stochastic drift term

Abstract: For applications in finance, we study the stochastic differential equation dXs = (2βXs + δs) ds + g(Xs) dBs with β a negative real number, g a continuous function vanishing at zero which satisfies a Holder condition and δ a measurable and adapted stochastic process such that ∫t0 δu du < ∞ a.e. for all t ∈ ℝ+ and which may have a random correlation with the process X itself. In this paper, we concentrate on the Euler discretization scheme for such processes and we study the convergence in L1-supnorm and in ℋ1-norm towards the solution of the stochastic differential equation with stochastic drift term. We also check the order of strong convergence. © 1998 John Wiley & Sons, Ltd.

Mixture of Weibull distributions - Parametric characterization of failure rate function

Abstract: A mixture distribution involving two two-parameter Weibull distributions is characterized by five parameters. The shape of the failure rate function for the mixture depends on the parameter values and can be one of eight distinct shapes. In this paper we present a complete parametric characterization of the shapes for the failure rate function for the mixture.

New concepts and algorithms for portfolio choice

Abstract: The paper studies the design of optimal (bond) portfolios taking into account various possible utility functions of an investor. The most prominent model for portfolio optimization was introduced by Markowitz. A real solution in this model can be achieved by quadratic programming routines for mean-variance analysis. Of course, there are many reasons for an investor to prefer other utility criteria than return/variance of return in the Markowitz model. In the last few years, many efficient multiple purpose optimization heuristics have been invented for the needs in optimizing telephone nets, chip layouts, job shop scheduling etc. Some of these heuristics have essential advantages: they are extremely flexible and very easy to implement on computers. One example of such an algorithm is the threshold-accepting algorithm (TA). TA is able to optimize portfolios under nearby arbitrary constraints and subject to nearly every utility function. In particular, the utility functions need neither to be convex, differentiable nor ‘smooth’ in any sense. We implemented TA for bond portfolio optimization with different utility criteria. The algorithms and computational results are presented. Under various utility functions, the ‘best’ portfolios look surprisingly different and have quite different qualities. Thus, for a portfolio manager it might be useful to provide himself with such a ‘multiple-taste’ optimizer in order to be able easily to readjust it according to his own personal utility considerations.