The Heston model is one of the most used techniques for estimating the fair value and the risk measures associated with investment certificates. Typically, the pricing engine implements a significant number of projections of the underlying until maturity, it calculates the pay-off for all the...

We study a small open economy displaying Pareto-distributed wealth resulting from random death. The government runs a distribution scheme on inheritance. We present the mathematical background that allows to study the dynamics of means. We end up with ordinary differential equations for the mean...

The valuation of options and to a large extent the financial derivatives market require an optimal estimation of the volatility, since this is precisely the variable that is negotiated. We present then a statistical methodology for the estimation of the volatility parameter for an asset using...

We propose a method for obtaining maximum likelihood estimates of parameters in diffusion models when the data is a discrete time sample of the integral of the process, while no direct observations of the process itself are available. The data are, moreover, assumed to be contaminated by...

We present a solution to the considered in [5] and [22] optimal stopping problem for some jump processes. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem where the normal reflection and smooth fit may break down and the latter then be...

A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic differential equations. We specify a parametric class of diffusions and estimate the parameters of interest by minimizing criteria based on the integrated squared difference between kernel...

This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochastic volatility models and counting process models. The diffusions can potentially be non-stationary. Although our...

The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset's volatility is a linear function of the asset value and the model garantees positive asset prices. In this paper it...