Binomial trees have been used extensively for broadcasting in clusters of workstations. In the case of heterogeneous nondedicated clusters and grid environments, the broadcasting occurs over a heterogeneous network, and the performance obtained by the broadcast algorithm will depend on the organization of the nodes onto the binomial tree. The organization of the nodes should take into account t...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...

Based on the theory of real options, this paper establishes a investment decision-making model that could evaluate the development of CCS considering some uncertainties: feed-in tariff, the clean price, carbon price, incentives and subsidies from the government and the progress of technology. This model calculates the investment value of CCS project by studying the binomial tree model of real o...

Continuously Paying Options (CPOs) form a very natural class of derivatives for hedging risks coming from adverse movements of a continuously traded asset. We study the rate of convergence of CPOs evaluated under the binomial tree scheme when the payout function φ is piecewise C subject to some boundedness conditions. We show that if φ is continuous, the rate of convergence is n−1 while it is n...

Mathematical models have been used to understand the transmission dynamics of infectious diseases and to assess the impact of intervention strategies. Traditional mathematical models usually assume a homogeneous mixing in the population, which is rarely the case in reality. Here, we construct a new transmission function by using as the probability density function a negative binomial distributi...

The theory of modular binomial lattices enables the simultaneous combinatorial analysis of finite sets, vector spaces, and chains. Within this theory three generalizations of Stifling numbers of the second kind, and of Lah numbers, are developed. 1. Stirling numbers and their formal generalizations The nota t ional convent ions of this paper are as follows: N = {0,1,2 . . . . }, P = {1,2,. . . ...

This article discusses convergence problems when calculating Vega (option sensitivity to volatility) that arise from discretization errors embedded in the lattice approach. Four alternative improvements to the traditional binomial method are discussed and investigated for performance. We also propose a new Modified Binomial (MB) Method to calculate Vegas. Numerical results show that although th...

Software pricing has traditionally been focused on the vendor’s internal business objectives of covering costs, achieving specified margins, and meeting the competition. Pricing methods such as flat price, tiered pricing, MIPS-based, usage-based, per user, per seat, and pay as you go, are often tactical in nature and easily matched by competitors, which can undermine profitability by accelerati...

A special inequality between the tail probabilities of certain related hypergeometrics was shown by Seneta and Phipps [19] to suggest useful ‘quasi-exact’ alternatives to Fisher’s [5] Exact Test. With this result as motivation, two inequalities of Hájek and Havránek [6] are investigated in this paper and are generalised to produce inequalities in the form required. A parallel inequality in bino...

In this paper we provide a closed-form approximation as well as a measure of the error for the price of several twodimensional derivatives under the assumptions of stochastic correlation and constant volatility. The method is applied to the pricing of Spread Options and Quantos Options, while three models for the stochatsic correlation are considered.