We study two-dimensional self-similar Ito diffusions (X,Y) whose margins are Wiener processes. We characterize the copulas of the random pairs (Xt,Yt) for a given t.

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman...

The nonparametric estimation of first and second infinitesimal moments describe by using the reweighted Nadaraya-Watson of scalar diffusion model. We used the symmetric kernels instead of standard kernel smoothing. We prove that the proposed estimators are consistence and asymptotically follow...

The present paper is concerned with the optimal control of stochastic differential equations, where uncertainty stems from one or more independent Poisson processes. Optimal behavior in such a setup (e.g., optimal consumption) is usually determined by employing the Hamilton-Jacobi-Bellman...

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman...

We propose a new test for a multivariate parametric conditional distribution of a vector of variables yt given a conditional vector xt. The proposed test is shown to have an asymptotic normal distribution under the null hypothesis, while being consistent for all fixed alternatives, and having...

Commodity price is an important factor for mining companies, as price volatility is a key parameter for mining project evaluation and investment decision making. The conventional discounted cash flow (DCF) methods are broadly used for mining project valuations, however, based on commodity price...

We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside the chemostat. We establish the Fokker–Planck...

Understanding the behaviour of market prices is not simple. Stock market prices tend to have complicated distributions with strong skewness and fat tails. One important step in forecasting tomorrow’s price is to estimate the volatility, i.e. how much tomorrow’s price is expected to differ...