In this paper we develop a class of applied probabilistic continuous time but discretized state space decompositions of the characterization of a multivariate generalized diffusion process. This decomposition is novel and, in particular, it allows one to construct families of mimicking classes...

Investors sometimes have strong convictions that a distinctive economic regime will prevail in the period ahead and therefore would like to form a portfolio that reflects the expected returns, standard deviations, and correlations of assets during such a regime. To do so, they typically isolate...

A framework is set up in which linear regression, as a way of approximating a random variable by other random variables, can be carried out in a variety of ways, which moreover can be tuned to the needs of a particular model in finance, or operations research more broadly. Although the idea of...

In this paper it is proved that the Black-Scholes implied volatility satisfies a second order non-linear partial differential equation. The obtained PDE is then used to construct an algorithm for fast and accurate polynomial approximation for Black-Scholes implied volatility that improves on the...

The aim of this paper is to investigate the ability of the Dynamic Variance Gamma model, recently proposed by Bellini and Mercuri (2010), to evaluate option prices on the S&P500 index. We also provide a simple relation between the Dynamic Variance Gamma model and the Vix index. We use this...

The fuzzy transform (F-transform), introduced by I. Perfilieva, is a powerful tool for the construction of fuzzy approximation models; it is based on generalized fuzzy partitions and it is obtained by minimizing a quadratic (L₂-norm) functional. In this paper we describe an analogous...

This article presents a novel combination of robust optimization developed in mathematical programming, and robust parameter design developed in statistical quality control. Robust parameter design uses metamodels estimated from experiments with both controllable and environmental inputs...

The four most readily available tests of autocorrelation in dynamic models namely Durbin's M test, Durbin's H test, Breusch - Godfrey (BGF) test and Ljung and Box (Q) test are compared in terms of their power for varying sample sizes, levels of autocorrelation and significance using Monte Carlo...

We study an expansion of the cumulative distribution function of the standard normal random variable that results in a family of closed form approximations that converge at 0. One member of the family that has only five explicit constants offers the absolute error of 5.79 10^{-6} across the...

Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the: (a) consistency,...