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1

OPTIMUM INVESTMENT RATE UNDER DIFFERENT DEMOGRAPHIC CONDITIONS

100%
Kliber P.
Ekonomista
|
2004
|
issue 4
501-519
EN
The article dwells on theoretical analysis of optimum investment trajectories in growth models in which the rate of population change varies. Two sets of assumptions were adopted to study the implications of abandoning the fixed rate of population increase condition. The first assumes that the rate is exogenous and does not depend on the level of wealth. The second assumes that population growth rate diminishes together with the increase of output per capita. Optimum investment trajectories for both assumptions were calculated and compared with the traditional results. Optimum investment policies, arrived at for non-malthusian models, markedly differ from the classical ones. The paths of those optimal trajectories depend on the way the population growth rate is introduced into the models (exogenously or endogenously).
2

QUANTILE HEDGING IN THE STOCHASTIC VOLATILITY MODEL

100%
Kliber P.
Przegląd Statystyczny
|
2006
|
vol. 53
|
issue 1
49-68
EN
In this paper we deal with quantile hedging of derivatives in the stochastic volatility (SV) models. We assume that temporary volatility of the stock prices is AR(1) process (autoregressive process of order 1). Then we formulate the problem of maximizing the expected success coefficient regarded that the cost of the hedging is limited. We describe how to solve this problem using dynamical programming method. Then we show empirical results for Polish stock market and compare the quality of the quantile hedging with the hedging based on Black-Scholes model
3

QUANTILE HEDGING OF THE EUROPEAN OPTION IN THE COX-RUBINSTEIN MODEL

100%
Kliber P.
Przegląd Statystyczny
|
2005
|
vol. 52
|
issue 4
60-77
EN
The article concerns the quantile hedging of an European option in the Cox-Rubinstein model. After introducing the problem of hedging a derivative instrument, two problems of quantile hedging were formulated. Then, using the method based on a martingale measure, the optimal success coefficient for hedging European option were derived. Finally, the results of empirical research concerning the quality of the quantile hedging the warrants from the Polish stock market were given. In this empirical research the Monte Carlo method with the bootstrap samples was used
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