We consider a fractional-order differential equation involving fractal activity time to represent the stochastic behaviour of a log-price process of an underlying asset. The log-price process is defined in terms of fractional integration of the fractional derivative of Brownian motion on fractal...

This paper uses linear programming to numerically evaluate the Laplace transform of the exit time distribution and the resolvent of the moments of various Markov processes in bounded regions. The linear programming formulation is developed from a martingale characterization of the processes and...

In this paper we study the dividend optimization problem for a corporation or a financial institution when the management faces (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting processes, Ornstein–Uhlenbeck and square-root...

<Para ID="Par1">A discrepancy function provides for an evaluation of a candidate model by quantifying the disparity between the candidate model and the true model that generated the observed data. The favored model from a candidate class is the one judged to have minimum discrepancy with the true model. The...</para>

<Para ID="Par1">We give sufficient conditions which the mutation rate must satisfy for the convergence of the genetic algorithm when that rate is allowed to change throughout iterations. The empirical performance of the algorithm with regards to changes in the mutation parameter is explored via test functions,...</para>

<Para ID="Par1">High dimensional data sets are now frequently encountered in many scientific fields. In order to select a sparse set of predictors that have predictive power and/or provide insightful understanding on which predictors really influence the response, a preliminary variable screening is typically...</para>

A threshold stochastic volatility (SV) model is used for capturing time-varying volatilities and nonlinearity. Two adaptive Markov chain Monte Carlo (MCMC) methods of model selection are designed for the selection of threshold variables for this family of SV models. The first method is the...