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

  • Karachanskaya Elena V., elena_chal@mail.ru Far Eastern State Transport University, 47 Serysheva Street, Khabarovsk 680027, Russia; Pacific National University, 136 Tikho-Okeanskaya Street, Khabarovsk 680035, Russia
  • Petrova Alena P., alyona.petrova393@gmail.com North-Eastern Federal University, 48 Kulakovsky Street, Yakutsk 677000, Russia
Keywords: programmed control with probability 1, stochastic Itô’s equation with jumps, first integral of system of the Itô equations, investment portfolio model, interest rate model

Abstract

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 Itˆo 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.

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How to Cite
Karachanskaya, E. and Petrova, A. ( ) “Modeling of the programmed control with probability 1 for some financial tasks”, Mathematical notes of NEFU, 25(1), pp. 25-37. doi: https://doi.org/10.25587/SVFU.2018.1.12766.
Section
Mathematics