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...

The security dynamics described by the Black-Scholes equation with price-dependent variance can be approximated as a damped discrete-time hopping process on a recombining binomial tree. In a previous working paper, such a nonuniform tree was explicitly constructed in terms of the continuous-time variance. The present note outlines how the previous procedure could be extended to multifactor Blac...

We prove that the expectation of the binomial distribution of order k with success probability p is monotonically increasing with respect to p for all n and k. The result is extended to the problems on exchangeable random sequences and expectations of distributions of mixtures of binomial distributions of order k are studied. If the mixing measure is stochastically increasing with respect to it...

This research investigates how the price frame affects the consumer’s preference. Using qualitative methodology from the prospective of behavioral science, we find in the overall assessment of a product, the consumers have more selective attention and thus higher weight on secondary attributes under partitioned pricing than under combined pricing. That means in online selling, consumers pay mor...

The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox–Ross–Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an opt...

Research ...nds that ...rms’ investment decisions are distorted by irreversibility and ...nance constraints. Whereas the existing literature examines the e¤ects of these features separately, this paper studies their interaction. The impact of these constraints on a ...rm’s incentive to invest is characterised using option pricing techniques. Financial constraints reduce the initial capacity, ra...

We present new families of lower bounds for the price of the American put option on a dividend paying stock when the stock follows a log normal process and the option can be exercised continuously to a finite horizon . By put call parity, these bounds can be easily converted to bounds on the price of the Ameican call option on a dividend paying stock. By numerically optimizing these bounds, we ...

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 ...

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.