We consider a (B, S)-security market with standard riskless asset B(t) = B0ert and risky asset S(t) with stochastic volatility depending on time t and the history of stock price over the interval [t − τ, t]. The stock price process S(t) satisfies a stochastic delay differential equation (SDDE) with past-dependent diffusion coefficient. We state some results on option pricing in such a market an...

We consider the nonlinear neutral functional differential equation [r (t)[x(t) + b a p(t, µ)x(τ(t, µ))dµ] (n−1) ] + δ d c q(t, ξ)f (x(σ (t, ξ)))dξ = 0 with continuous arguments. We will develop oscillatory and asymptotic properties of the solutions. have studied the oscillation theory of second-order and higher-order neutral functional differential equations, in which the highest-order derivati...

One of the important problems in the qualitative theory of functional differential equations of neutral type, which has currently received wide attention, is to discuss the existence of solutions, either oscillatory or nonoscillatory, of the equation under consideration. As far as the nonoscillatory solutions are concerned, there has been a lot of systematic investigations, and numerous results...

This article is mainly devoted to the study of existence solutions for second-order abstract non-autonomous integro-differential evolution equations with infinite state-dependent delay. In first part, we are concerned retarded functional differential second extend our results neutral Our established using properties resolvent operator corresponding equation and fixed point theorems. Finally, an...