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

We present a brief survey of the main results obtained by V. S. Korolyuk in probability theory and mathematical statistics.     

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

We study the problem of stability of semi-Markov evolution systems and its application in financial mathematics.     

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

We investigate the asymptotic stability of semi-Markov risk processes with probability one in schemes of averaging and diffusion approximation. International Mathematical Center, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 972–979, July, 1999.     

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

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.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 7, pp. 976–983, July, 1995.The work was partially supported by Grant No. K43100 from the Joint Fund of the Government of Ukraine and the International Science Foundation.     

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

We consider problems of optimal stabilization of controlled evolution stochastic systems in semi-Markov media and their application to financial stochastic models. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 687–698, May, 1998.