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...

We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross...

Since January 2005, pensions in Slovakia are operated by a three-pillar system. This paper concentrates on the mandatory, fully funded second pillar. We recall the dynamic stochastic accumulation model proposed in [9]. Pension asset managers are very cautious and hold low stocks proportions in...

In life-cycle economics the Samuelson paradigm (Samuelson, 1969) states that the optimal investment is in constant proportions out of lifetime wealth composed of current savings and the present value of future income. It is well known that in the presence of credit constraints this paradigm no...

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 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...