In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X,N) follows the BGG law if N has geometric...

Abstract In this paper we introduce the well-balanced Lévy driven Ornstein–Uhlenbeck process as a moving average process of the form X t  = ∫ exp(- λ | t - u |) dL u . In contrast to Lévy driven Ornstein–Uhlenbeck processes the well-balanced form possesses continuous sample paths and...

The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property is manifested by the random (infinitely...

We show that the stochastic domination of an infinitely divisible random variable X by another infinitely divisible random variable Y does not imply, generally speaking, a comparison between their corresponding Lévy measures.