Stability of stochastic delay equations of Itô form with jumps and Markovian switchings, and their applications in finance. (English. Ukrainian original) Zbl 0998.60059

Svishchuk, A. V.; Kazmerchuk, Yu. I.

Theory Probab. Math. Stat. 64, 167-178 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 141-151 (2001).

The main contributions of this article are results about existence, uniqueness and stability of processes defined by stochastic delay equations with Poisson jumps and Markovian switchings. In order to prove such results an extension of the second Lyapunov method for stochastic differential equations is successfully used. In applications the authors focus on financial analysis and obtain new results concerning stability of delay financial models.

Reviewer: N.M.Zinchenko (Kyïv)

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
93E15	Stochastic stability in control theory
62P05	Applications of statistics to actuarial sciences and financial mathematics

Keywords:

stability; stochastic delay equations; Poisson jumps; Markovian switchings; Lyapunov method; financial models