The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of generalized Black-Scholes equations. We analyze...

In this review paper we recall a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. The model has been proposed and analyzed by the authors. We assume stock prices to be driven by a geometric Brownian...

In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration....

In this paper we generalize and analyze the model for pricing American-style Asian options due to Hansen and Jorgensen by including a continuous dividend rate q and a general method of averaging of the floating strike. We focus on the qualitative and quantitative analysis of the early exercise...

The purpose of this paper is to construct the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility depending on the option price. We review a method how to transform the problem into a solution of a time depending nonlinear parabolic equation...

The purpose of this paper is to study the generalized Fong - Vasicek two-factor interest rate model with stochastic volatility. In this model the dispersion of the stochastic short rate (square of volatility) is assumed to be stochastic as well and it follows a non-negative process with...

Since January 2005, pensions in Slovakia are operated by a three-pillar system proposed by the World Bank. The paper discusses and mathematically captures principles of the pension reform in Slovakia. We also discuss the impact of the reform on the deficit of the pension system. We mainly focus...

The aim of this paper is to assess the expected socio-economic impacts of various scenarios of pandemic influenza mitigation on the economy and mortality for Slovakia. The paper relies on data accessible in the literature as well as on data supplied by pharmaceutical and health insurance...

We analyze analytic approximation formulae for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a volatility nonlinearly depending on the interest rate itself. We derive the order of accuracy of the analytical...