Consequences of an incorrect model specification on population growth

We consider stochastic differential equations to model the growth of a population ina randomly varying environment. These growth models are usually based on classical deterministic models, such as the logistic or the Gompertz models, taken as approximate models of the "true" (usually unknown) growth rate. We study the effect of the gap between the approximate and the "true" model on model predictions, particularly on asymptotiv behavior and mean and variance of the time to extinction of the population

Speed and Accuracy Comparison of Noncentral Chi-Square Distribution Methods for Option Pricing and Hedging under the CEV Model

Pricing options and evaluating greeks under the constant elasticity of variance (CEV) model require the computation of the noncentral chi-square distribution function. In this article, we compare the performance in terms of accuracy and computational time of alternative methods for computing such probability distributions against an xternally tested benchmark. In addition, we present closed-form solutions for computing greek measures under the CEV option pricing model for both beta 2, thus being able to accommodate direct leverage effects as well as inverse leverage effects that are frequently observed in the options markets

Individual Growth in a Random Environment: an optimization problem

We consider a class of stochastic differential equations model to describe individual growth in a random environment. Applying these models to the weight of mertolengo cattle, we compute the mean profit obtained from selling an animal to the meat market at different ages and, in particular, determine which is the optimal selling age. Using first passage time theory we can characterize the time taken for an animal to achieve a certain weight of market interest for the first time. In particular, expressions for the mean and standard deviation of these times are presented and applied to real data. These last results can be used to determine the optimal selling weight in terms of mean profit