We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. This includes the existence of Esscher martingale measures and martingale measu...

Abstract: We use the martingale method to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, we obtain bounds on certain martingale differences associated with the random sequences, which may be of independent interest. As an applicatio...

In this paper we study the stationary distributions for reflected diffusions with jumps in the positive orthant. Under the assumption that the stationary distribution possesses a density in R+ that satisfies certain finiteness conditions, we characterize the Fokker-Planck equation. We then provide necessary and sufficient conditions for the existence of a product-form distribution for diffusion...

The stock price process is modelled by a geometric Lévy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However the model can be completed by the so called power-jump assets. By doing this we allow investment in these new assets and we can try t...

We study Girsanov’s theorem in the context of symmetric Markov processes, extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov transformations of “gradient type”. We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward-backward martingale method of Lyons-Zheng, to cover the cas...

Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps. AMarkov pure jumpmodel is formulated on making variance gamma parameters deterministic functions of the price level. Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation. The motion is decomposed into a space dependent drift a...

Let X be a Hilbert-space valued martingale and Y a real-valued supermartingale which are orthogonal and with Y diierentially subordinate to X. Then where the constant (2) is Catalan's constant whose approximate value is 0:915965594. The constant K is B. Davis' constant in the Kolmogorov's weak-type inequality for conjugate harmonic functions in the unit disk. The inequality is sharp.