Despite its success, the Black-Scholes formula has become increasingly unreliable over time in the very markets where one would expect it to be most accurate. In addition, attempts by financial economists to extract probabilistic information from option prices have been puny in comparison to what is clearly possible. This paper develops a new method for inferring risk-neutral probabilities (or ...

The scattering number of a graph G, denoted sc(G), is defined by sc(G)=max{c(G−S)− |S| : S ⊆ V(G) and c(G−S)≠ 1} where c(G−S) denotes the number of components in G− S. It is one measure of graph vulnerability. In this paper, general results on the scattering number of a graph are considered. Firstly, some bounds on the scattering number are given. Further, scattering number of a binomial tree i...

A wide range of graphs with regular structures are shown to be embeddable in an injured hypercube with faulty links. These include rings, linear paths, binomial trees, binary trees, meshes, tori, and many others. Unlike many existing algorithms which are capable of embedding only one type of graphs, our algorithm embeds the above graphs in a uniied way, all centered around a notion called edge ...

The binomial tree method, first proposed by Cox, Ross, and Rubinstein [Journal of Financial Economics, 7 (1979), pp. 229–263], is one of the most popular approaches to pricing options. By introducing an additional path-dependent variable, such methods can be readily extended to the valuation of path-dependent options. In this paper, using numerical analysis and the notion of viscosity solutions...

The pricing models of American-type path-dependent options are of degenerate parabolic obstacle problems. The binomial tree method is the most popular approach to pricing options. For some special cases, this method is modified in order to make it feasible. The main purpose of this paper is, using numerical analysis and the notion of viscosity solutions, to show the uniform convergence of the b...

We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately repr...

Modern networks typically limit the size of the largest packet for efficient communication. Thus, long messages are packetized and transmitted. Such networks also provide network interface support for nodes, which typically includes a coprocessor and memory, to implement the lower layers of the communication protocol. This paper presents a concept of smart network interface support for packetiz...

In a variety of research domains, data are generated as a consequence of the count process and may possess an ‘excess’ of zeros. There have been many attempts to analyse such data using different statistical methods, including the zero-inflated Poisson (ZiP) and zero-inflated binomial (ZiB) models. The interpretation of these models is however problematic if the covariates considered for the no...