2019
Том 71
№ 11

All Issues

Svishchuk A. V.

Articles: 13
Article (Ukrainian)

Stochastic Stability of Processes Determined by Poisson Differential Equations with Delay

Svishchuk A. V., Svishchuk M. Ya.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

On the Creative Contribution of V. S. Korolyuk to the Development of Probability Theory

Bratiichuk N. S., Gusak D. V., Svishchuk A. V.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Analog of the black-scholes formula for option pricing under conditions of (B, S, X)-incomplete market of securities with jumps

Kalemanova A. V., Svishchuk A. V., Zhuravyts'kyi D. G.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Stability of semi-Markov risk processes in schemes of averaging and diffusion approximation

Goncharova S. Ya., Svishchuk A. V.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

Filtration of components of processes of random evolution

Lukin A. E., Svishchuk A. V.

↓ Abstract   |   Full text (.pdf)

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 tt);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.

Article (Ukrainian)

Optimal control over evolution stochastic systems and its application to stochastic models of financial mathematics

Biirdeinyi A. G., Svishchuk A. V.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Stability of semi-markov evolution systems and its application in financial mathematics

Biirdeinyi A. G., Svishchuk A. V.

↓ Abstract   |   Full text (.pdf)

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.

Article (English)

Hedging of options under mean-square criterion and semi-Markov volatility

Svishchuk A. V.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Weak convergence of semi-Markov random evolutions in an averaging scheme (martingale approach)

Svishchuk A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1680–1686

Article (Ukrainian)

Limiting representation of continuous semi-Markov random evolutions in the series scheme

Korolyuk V. S., Svishchuk A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 11. - pp. 1476–1482

Article (Ukrainian)

A central limit theorem for nonhomogeneous semi-Markov random evolutions

Korolyuk V. S., Svishchuk A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1064–1070

Article (Ukrainian)

Central limit theorem in the phase extension scheme for semi-Markov random evolutions

Korolyuk V. S., Korolyuk V. V., Svishchuk A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 316–321

Article (Ukrainian)

Central limit theorem for Semi-Markov random evolutions

Korolyuk V. S., Svishchuk A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 330–334