While the volatility of portfolios are often modeled by continuous Brownian motion processes, discontinuous jump processes are more appropriate for modeling important external events that significantly affect the prices of financial assets. Here the discontinuous jump processes are modeled by state and control dependent compound Poisson processes, such that the random jumps come at the times of...

In many (if not most) real-world applications, the arrival of customers to a service center is not well described by renewal processses. Quite often, the times between successive arrivals are correlated, whereas renewal processes have independent interarrival times. A natural generalization is the class of semiMarkov processes (SMP), which when specifically applied to the arrival of customers a...

This article presents a stochastic model of lymphocyte recruitment in inflamed brain microvessels. Recent studies about the inflammatory process of the brain that leads to multiple sclerosis have revealed that lymphocyte extravasation is a sequence of dynamical states, mediated by partially overlapped interactions of different adhesion molecules and activation factors. This study’s model of lym...

In this paper, a discount model is proposed to coordinate pricing and ordering decisions in a two-echelon supply chain (SC). Demand is stochastic and price sensitive while lead times are fixed. Decentralized decision making where downstream decides on selling price and order size is investigated. Then, joint pricing and ordering decisions are extracted where both members act as a single entity ...

The Doob–Meyer decomposition theorem opened the way towards the theory of stochastic integration with respect to square integrable martingales and—consequently—semimartingales, as described in the seminal paper [7]. According to Kallenberg [4], this theorem is “the cornerstone of the modern probability theory”. It is therefore not surprising that many proofs of it are known. To the author’s kno...