Modeling of the programmed control with probability 1 for some financial tasks

The description of the dynamics of some financial events can be related to Itô stochastic differential equations (SDE). In this paper, we consider a financial model affected by random disturbances which take the form of Wiener and Poisson perturbations. The construction of the programmed control with probability 1 (PCP1) is based on the concept of first integral for stochastic dynamic systems of diffusion type with jumps which are described by the Itô equations. Two types of financial models are considered as examples of the construction of PCP1: the investment portfolio model (diffusion model) and the interest rate model (diffusion with jumps). The given examples are accompanied by numerical modeling.