منابع مشابه
Research Article Jump Telegraph Processes and Financial Markets with Memory
The paper develops a new class of financial market models. These models are based on generalized telegraph processes with alternating velocities and jumps occurring at switching velocities. The model under consideration is arbitrage-free and complete if the directions of jumps in stock prices are in a certain correspondence with their velocity and with the behaviour of the interest rate. A risk...
متن کاملA Damped Telegraph Random Process with Logistic Stationary Distribution
We introduce a stochastic process that describes a finite-velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the probability law of the motion, which admits a logistic stationary limit in a special case. Various results on the distribut...
متن کاملJump processes
Although historically models in mathematical finance were based on Brownian motion and thus are models with continuous price paths, jump processes play now a key role across all areas of finance (see e.g. [5]). One reason for this move into a new class of processes is that because of their distributional properties diffusions in many cases cannot provide a realistic picture of empirically obser...
متن کاملStructured Proportional Jump Processes
Learning the association between observed variables and future trajectories of continuoustime stochastic processes is a fundamental task in dynamic modeling. Often the dynamics are non-homogeneous and involve a large number of interacting components. We introduce a conditional probabilistic model that captures such dynamics, while maintaining scalability and providing an explicit way to express...
متن کاملJump-type Lévy processes
The assumption that observations are normally distributed is predominant in many areas of statistics. So is the situation with time series of financial data where from the very beginning of continuous-time modeling Brownian motion itself or geometric Brownian motion became the favorites. This is largely due to the fact that the normal distribution as well as the continuous-time process it gener...
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ژورنال
عنوان ژورنال: Statistics & Probability Letters
سال: 2013
ISSN: 0167-7152
DOI: 10.1016/j.spl.2013.06.018