Svishchuk A. V.
Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 413-418
We prove an existence theorem and establish the property of stochastic stability for processes determined by the Poisson stochastic differential equations with delay.
Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1014-1030
We present a brief survey of the main results obtained by V. S. Korolyuk in probability theory and mathematical statistics.
Analog of the black-scholes formula for option pricing under conditions of (B, S, X)-incomplete market of securities with jumps
Ukr. Mat. Zh. - 2000. - 52, № 3. - pp. 424-431
We describe a (B, S,X )-incomplete market of securities with jumps as a jump random evolution process that is a combination of an ltô process in random Markov medium and a geometric compound Poisson process. For this model, we derive the Black-Scholes equation and formula, which describe the pricing of the European call option under conditions of (B,S,X)-mcomplete market.
Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 972–979
We investigate the asymptotic stability of semi-Markov risk processes with probability one in schemes of averaging and diffusion approximation.
Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1701–1705
The problem of estimation of a nonobservable component θt for a two-dimensional process (θt, ξt) of random evolution (θ t,ξt);xt, 0≤t≤T, is investigated on the basis of observations of ξs. s≤t, where x t is a homogeneous Markov process with infinitesimal operator Q. Applications to stochastic models of a (B,S)-market of securities is described under conditions of incomplete market.
Optimal control over evolution stochastic systems and its application to stochastic models of financial mathematics
Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 687–698
We consider problems of optimal stabilization of controlled evolution stochastic systems in semi-Markov media and their application to financial stochastic models.
Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1386-1401
We study the problem of stability of semi-Markov evolution systems and its application in financial mathematics.
Ukr. Mat. Zh. - 1995. - 47, № 7. - pp. 976–983
We consider a problem of hedging of the European call option for a model in which the appreciation rate and volatility are functions of a semi-Markov process. In such a model, the market is incomplete.
Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1680–1686
Ukr. Mat. Zh. - 1989. - 41, № 11. - pp. 1476–1482
Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1064–1070
Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 316–321
Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 330–334