10 research outputs found
Linear Control Systems on Unbounded Time Intervals and Invariant Measures of Ornstein--Uhlenbeck Processes in Hilbert Spaces
Full text link
O warunkowaniach dla zbieżnych do zera ciągów wektorów losowych w przestrzeniach Banacha
No full texthttps://doi.org/10.26485/0459-6854/2018/68.3/1
Wycena opcji w modelu CRR z parametrami zależnymi od czasu dla dwóch jednostek czasu – cześć II
No full textIn the second part of the paper we prove the convergence of option prices in the presented model to the price that is given by some formula corresponding to the Black-Scholes formula
Wycena opcji w modelu CRR z parametrami zależnymi od czasu dla dwóch jednostek czasu – cześć I
No full textIn this paper we present some generalization of the Cox-Ross-Rubinstein (CRR) option pricing model. We assume that two parameters of the model (an interest rate of a bank account and a volatility of the logarithm of the stock price’s changes) are different in each of two analyzed periods of time.W pracy przedstawiono pewien uogólniony model Coxa-Rossa-Rubinsteina na wycenę opcji. Założono, że dwa parametry modelu (stopa procentowa oraz współczynnik zmienności logarytmu cen akcji-volatility) zmieniają się w każdej z dwóch jednostek czasu
On Ornstein-Uhlenbeck Generators
No full text. The aim of this paper is to investigate properties of the generator L of the general nonsymmetric Ornstein-Uhlenbeck semigroup possessing an invariant measure. First we give the necessary and sufficient conditions for the Logarithmic Sobolev Inequality, which extend the result of Simon to the nonsymmetric case. Next, we present conditions for the domains of L and L to have continuous imbeddings into the Sobolev spaces W 2;2 Q1 and W 1;2 Q and into the Orlicz spaces L p LogL r , thus extending the results known for the diagonal or symmetric case. We characterize the cores of the generators L and L and obtain certain factorizations of L and L which generalize the representation of the Malliavin operator. The necessary and sufficient condition for compactness of the imbedding of the Sobolev space W 1;2 Q into L 2 is also given. Finally we give necessary and sufficient conditions for L to be symmetric. The domains are characterized more explicitly in this case. * ..
