We consider models for stock prices which relates to random processes with independent homogeneous increments (Levy processes). These models are arbitrage free but correspond to the incomplete financial market. There are many different approaches for pricing of financial derivatives. We consider...

We extend some known results on a relation between the distribution tails of the continuous local martingale supremum and its quadratic variation to the case of locally square integrable martingale with bounded jumps. The predictable and optional quadratic variations are involved in the main result.

We discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time...

Solving some integro-differential equation we find the Laplace transformation of the first passage time for Filtered Poisson Process generated by pulses with uniform or exponential distributions. Also, the martingale technique is applied for approximations of expectations accuracy is veryfying...

We find a solution of the optimal stopping problem for the case when a reward function is an integer function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing time through a level defined as the largest root of Appell's polynomial...

We consider a finite simple point process in space Rd evolving in discrete time in the following way. Starting with an arbitrary initial configuration, at each time step a point is chosen at random from the process according to a certain distribution, and then k new points are added to the...