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...

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...