http://dspace.nbuv.gov.ua:80/handle/123456789/4546 2026-04-06T01:49:12Z http://dspace.nbuv.gov.ua:80/handle/123456789/4576 Risk process with stochastic premiums Zinchenko, N.; Andrusiv, A. The Cramer-Lundberg model with stochastic premiums which is natural generalization of classical dynamic risk model is considered. Using martingale technique the Lundberg inequality for ruin probability is proved and characteristic equations for Lundberg coefficients are presented for certain classes of stochastic premiums and claims. The simple diffusion and de Vylder approximations for the ruin probability are introduced and investigated similarly to classical Cramer-Lundberg set-up. The weak and strong invariance principles for risk processes with stochastic premiums are discussed. Certain variants of the strong invariance principle for risk process are proved under various assumptions on claim size distributions. Obtained results are used for investigation the rate of growth of the risk process and its increments. Various modifications of the LIL and Erdos-Renyi-type SSLN are proved both for the cases of small and large claims. 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4575 On the rate of convergence of barrier option prices in binomial market to those in continuous time market Soloveiko, O.; Shevchenko, G. We estimate the rate of convergence of barrier option price in a discrete time binomial market to such in a continuous time market. 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4574 Nonlinearly perturbed stochastic processes Silvestrov, D. This paper is a survey of results presented in the recent book [25]). This book is devoted to studies of quasi-stationary phenomena in nonlinearly perturbed stochastic systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on new types of asymptotic expansions for perturbed renewal equation and recurrence algorithms for construction of asymptotic expansions for Markov type processes with absorption are presented. Asymptotic expansions are given in mixed ergodic (for processes) and large deviation theorems (for absorption times) for nonlinearly perturbed regenerative processes, semi-Markov processes, and Markov chains. Applications to analysis of quasi-stationary phenomena in nonlinearly perturbed queueing systems, population dynamics and epidemic models, and risk processes are presented. The book also contains an extended bibliography of works in the area. 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4573 Reselling of European option if the implied volatility varies as Cox-Ingersoll-Ross process Pupashenko, M.; Kukush, A. On Black and Scholes market Investor buys a European call option. At each moment of time till the maturity he is allowed to resell the option for the quoted market price. In Kukush et al. (2006) On reselling of European option, Theory Stoch. Process., 12(28), 75-87, a similar problem was investigated for another model of the market price. We propose a more realistic model based on Cox-Ingersoll-Ross process. Discrete approximation for this model is investigated, which is arbitrage–free. For this discrete model, a formula for penultimate optimal stopping domains is derived. 2008-01-01T00:00:00Z