In the present paper we consider a model for stock prices which is a generalization of the model behind the Black-Scholes formula for pricing European call options. We model the log-price as a deterministic linear trend plus a diffusion process with drift zero and with a diffusion coefficient...

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...

We consider financial markets with agents exposed to an external source of risk which cannot be hedged through investments on the capital market alone. The sources of risk we think of may be weather and climate. Therefore we face a typical example of an incomplete financial market. We design a...

For stochastic differential equations reflecting on the boundary of a connected interval in R we discuss the problem of approximation for solutions. The main results are convergence in law as well as in Lp of discrete schemes that fundamentally generalize the classical Euler and Euler–Peano...

In this work we study rough differential equations driven by a fractional Brownian motion with Hurst parameter H>14 and establish Varadhan’s small time estimates for the density of solutions of such equations under Hörmander’s type conditions.

In this study, the non-homogeneous Gompertz diffusion process (NHGDP) is used to model the monthly peak electricity demand in Mauritius in order to predict the future values on the basis of a Genetic Algorithm (GA) approach. Our model is developed based a key economic indicator which is the...

We study the parameter estimation of two-type continuous-state branching processes with immigration based on low frequency observations at equidistant time points. The ergodicity of the processes is proved. The estimators are based on the minimization of a sum of squared deviation about...

We develop a dynamic stochastic full equilibrium New Keynesian model of two open economies based on stochastic differential equations to analyse the interdependence between monetary policy and financial markets in the context of the recent Financial crisis. The effect of bubbles on stock and...

We develop further ideas on how to construct low-dimensional models of stochastic dynamical systems. The aim is to derive a consistent and accurate model from the originally high-dimensional system. This is done with the support of centre manifold theory and techniques. Aspects of several...

This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a...