Over the last decade or so, artificial neural networks (ANNs) have become one of the most promising tools formodelling hydrological processes such as rainfall runoff processes. However, the employment of a single model doesnot seem to be an appropriate approach for modelling such a complex, nonlinear, and discontinuous process thatvaries in space and time. For this reason, this study aims at de...

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...

At important events or announcements, there can be large changes in the value of financial portfolios. Events and their corresponding jumps can occur at random or scheduled times. However, the amplitude of the response in either case can be unpredictable or random. While the volatility of portfolios are often modeled by continuous Brownian motion processes, discontinuous jump processes are more...

In the paper a stochastic control model is studied, that admits a diffusion approximation. In the prelimit model the disturbances are given by noise processes of various types: additive stationary noise, rapidly oscillating processes, and discontinuous processes with large intensity for jumps of small size. We show that a feedback control, that satisfies a Lipschitz condition and is δ−optimal f...

At important events or announcements, there may be large changes in the value of market portfolios due to large fluctuations in the underlying assets. Events and their corresponding jumps can occur at random times or at scheduled times. However, the amplitude of the response to an event in either case can be unpredictable and thus can be considered as random. While the volatility of portfolios ...