In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Levy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Levy process.

In this paper we obtain the scaling limit of multidimensional Levy walk and describe the detailed structure of the limiting process. It occurs that the scaling limit is a subordinated alpha-stable Levy motion with the parent process and subordinator being strongly dependent processes. The...

The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property is manifested by the random (infinitely...

The paper deals with decision optimization of the integration of distributed generation with electrical grid. Presented algorithm is based on technical and economic factors of integration of distributed generation. The method is based on optimization of coordinates, which in this case are values...

In this paper we discuss subdiffusive mechanism for the description of some stock markets. We analyse the fractional Black–Scholes model in which the price of the underlying instrument evolves according to the subdiffusive geometric Brownian motion. We show how to efficiently estimate the...

The paper presents two algorithms of optimal placement of distributed generation in electrical grid. Both algorithms take into account technical and economic effectiveness of integration of distributed generation with the power grid. Methods, used in the algorithms, are based on the linear...

The paper deals with decision optimization of the integration of distributed generation with electrical grid. Presented algorithm is based on technical and economic factors of integration of distributed generation. A Linear Programming Methodology, where the various alternatives of distributed...

We develop a new class of continuous-time models based on the solutions of tempered fractional Langevin equations for Ornstein–Uhlenbeck process driven by Levy noise. We present methods of simulation of sample paths of such processes. We show how to use such models in modeling short term...

Because of the increasing number of distributed energy sources integrated with the distribution network various optimization methods are very useful in determining the optimal placement, type and size of the distributed generators. One of the most commonly used algorithms are so called...

In this paper we consider a generalization of one of the earliest models of an asset price, namely the Black–Scholes model, which captures the subdiffusive nature of an asset price dynamics. We introduce the geometric Brownian motion time-changed by infinitely divisible inverse subordinators,...