A pure birth stochastic process with several initial conditions is considered. We analyze multiplicity distributions of e+e− collisions and e-p collisions, usig the Modified Negative Binomial Distribution (MNBD) and the Laguerre-type distribution. Several multiplicity distributions show the same minimum χ2’s values in analyses by means of two formulas: In these cases, we find that a parameter N...

The paper investigates a discrete time Binomial risk model with different types of polices and shock events may influence some the claim sizes. It is shown that this can be considered as particular case classical compound model. As far we work parallel counting processes in infinite time, if consider them independent, probability event they to have at least once simultaneous jumps would equal o...

In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of...

The present time, denoted at n = 0 and the expiration time, denoted at n = N . The lower case letter n, k (and occasionally i, j,m) will be used to denote the time variable. The notation Sk (or Sn, Si, Sj · · · ) denotes the value of the stock (the underlying) at time k (or time n, i, j · · · ). An important convention we’ll use is that S0 will always be a constant, that is the present value of...

We present an elaboration of the usual binomial AR(1) process on {0, 1, . . . , N} that allows the thinning probabilities to depend on the current state n only through the “density” n/N , a natural assumption in many real contexts. We derive some basic properties of the model and explore approaches to parameter estimation. Some special cases are considered that allow for overand underdispersion...

By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive efficient Gibbs sampling inference. We show that the gamma-NB process can be reduced to the hierarchical Dirichlet process with normalization, highlighting its un...

The real estate derivatives market allows participants to manage risk and return from exposure to property, without buying or selling directly the underlying asset. Such market is growing very fast hence the need to rely on simple yet effective pricing models is very great. In order to take into account the real estate market sensitivity to the interest rate term structure in this paper is pres...

Process control schemes for multistream binomial processes are described. A multistream process is one in which the streams are uncorrelated or very weakly correlated. When each of the J streams are identical (a homogeneous multistream process) one can use a group control chart (a k-sigma p-chart on which only the largest and smallest of the J sample proportions nonconforming are plotted). A te...