A NOTE ON ARBITRAGE AND CLOSED CONVEX CONES

We give an example of a subspace K of     such that     , where     denotes the closure with respect to convergence in probablity. On the other hand, the cone   C ≔ K − L ^∞₊  is dense in   L ^∞  with respect to the weak-star topology  σ( L ^∞, L ¹)  . This example answers a question raised by I. Evstigneev. The topic is motivated by the relation of the notion of no arbitrage and the existence of martingale measures in Mathematical Finance.     

A Nonstandard Approach to Option Pricing

Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model.     

Futures and forward price differential and the effect of marking‐to‐market: Australian evidence

The objective of this paper is to examine the effects of marking‐to‐market of futures contracts on the price differential between futures and forward contracts based on the predictions of the Cox, Ingersoll and Ross (1981) (CIR) model. Cox et al ., (1981) derive a series of propositions with respect to the relationship between futures and forward prices and a set of testable implications. These are tested empirically in this paper using Australian data from November 1991 to June 1997. The results provide evidence of the presence of significant futures and forward price differences, where the futures price is consistently below the forward price. Only partial support is found for the Cox et al ., (1981) propositions, implying that the effect of marking‐to‐market is not able to fully account for the price differential. Therefore, it is not possible to rule out the influence of other institutional factors on the futures‐forward price difference.     

IPO高抑价之谜：“租金分配观”还是“定价效率观”？——基于2005-2012年数据

对中国IPO极高的抑价现象存在两种不同的解释——“定价效率观”和“租金分配观”。以2005—2012年A股IPO公司作为样本,对这两种观点进行检验,结果表明：“租金分配观”只在2005-2008年成立,在2009-2012年不成立;“定价效率观”则能更好地解释2005年实施询价配售制度以来中国IPO抑价率的变化。     

Research on reform tactics of China＇s oil price forming mechanism

The main problem the oil industry facing in modem market economy is unreasonable price mechanism, the substance of which should be attributed to the fact that it is still short of a reasonable oil price forming mechanism. Therefore, the discussion on this aspect should be pushed forward. As the breakthrough point, on the basis of status research in quo and formation causes of China＇s oil price forming mechanism, we should analyze the necessity and imminence of China＇s oil price forming mechanism reform deeply. Then, with the perspective of development strategy of the oil industry, we put forward the reform measures of it.     

The Motivation and Effectiveness of Gas Industry Economic Regulation in New South Wales, 1912–39

The oldest industry in Australia subjected to economic regulation is the gas supply industry in the state of New South Wales. In this paper the aims and motivation of the New South Wales Government in establishing the regulatory regime in 1912 and the subsequent effectiveness in achieving them are determined. Initially the regulatory regime was based on ad hoc arrangements, but eventually a more permanent structure was devised that effectively defused political controversy over gas market pricing and stabilised prices rather than substantially lowered them.