This paper analyzes some graph issues by using the symbolic program Mathematica and its version for theWeb, webMathematica. In particular, we consider the problem of graph coloring: the assignment of colors to the vertices/edges of the graph such that adjacent vertices/edges are colored differently. In addition, we address the problem of obtaining the tenacity of binomial trees with Mathematica...

A Dynamic Portfolio or Dynamic Asset Allocation is a strategy used to determine the proportion of a number of assets, chosen carefully, in order to achieve optimum performance of the portfolio. In this paper, the portfolio consists only Options traded in the financial market. One of the most famous models of option pricing is Binomial Cox-Ross-Rubinstein (CRR) Model. Using Fuzzy Binomial CRR pr...

This paper is concerned with the quantum properties of the binomial model (or, the CRR-model). We show that the single-step binomial model is incomplete in the quantum setting. All risk-neutral states of the single-step binomial model in the quantum setting are characterized. Moreover, it is shown that all single-step models are incomplete in the quantum setting. Therefore, incompleteness is ba...

Numerical valuation model is extended for European Asian options while considering the higher moments of the underlying asset return distribution. The Edgeworth binomial lattice is applied and the lower and upper bounds of the option value are calculated. That the error bound in pricing Asian options from the Edgeworth binomial model is smaller than the error bound model by Chalasani et al. is ...

Given a simple connected undirected graph G = (V , E), the Wiener index W (G) of G is defined as half the sum of the distances d(u, v) between all pairs of vertices u, v of G, where d(u, v) denotes the distance (the number of edges on a shortest path between u and v) between u, v in G. We obtain an expression for W (G), where G is a binomial tree. For Fibonacci trees and binary Fibonacci trees ...

In this article, we propose using a real options framework to model and financially value a cross-training policy. The cross-training policy involves a dynamic investment on workforce flexibility. We model it as an approximation of an American call option using binomial lattices. Value stems from the merit of dynamic cross-training compared with the deterministic case using traditional discount...

We amend some results in the literature. We verify a formula for the integrity of the binomial tree, and correct formulas for the integrity of the complete k-ary tree. Dedicated to Henda Swart with the greatest thanks.

The paper shows that variables commonly used in takeover prediction models also help to explain the likelihood of several other restructuring events, including divestitures, bankruptcies and significant employee layoffs. This finding helps to explain the larger misclassification errors in binomial takeover prediction models commonly used in prior research. The results show that modelling takeov...

T decision analysis methods can provide an intuitive approach to valuing projects with managerial flexibility or real options. The discrete-time approach to real-option valuation has typically been implemented in the finance literature using a binomial lattice framework. Instead, we use a binomial decision tree with risk-neutral probabilities to approximate the uncertainty associated with the c...

A generalized correlated random walk is a process of partial sums Xk = ∑kj=1 Yj such that (X, Y ) forms a Markov chain. For a sequence (X) of such processes in which each Y j takes only two values, we prove weak convergence to a diffusion process whose generator is explicitly described in terms of the limiting behaviour of the transition probabilities for the Y. Applications include asymptotics...