Efficiency has been a very important issue for financial markets all over the world ever since trading began in the stock exchanges. The most ardent market observers believe that although short-term inefficiencies remain, the financial markets are efficient in the long run. However, this question has not been investigated in terms of a theoretical model in detail. This issue has been addressed considering the two financial assets in order to obtain a rigorous definition of market efficiency. Through simulation and graphical verification, it is shown that the market is efficient in the long run, albeit in a simplistic setting. It explores alternative value generating processes by considering models with discrete jumps, heavy-tailed probability models and a regime-switching model.

One of the problems that has drawn the interest of all the market forces involved in trading, and which has a very high potential of affecting the academic thinking on investments, is that of market efficiency. The issue of efficiency is a very fundamental one, and is something which most of the market players would like to settle forever, so that they can make long-term decisions based on the notion of the market efficiency. Unless they do reckless speculation and trading momentum, the belief is that the market is efficient in the long run, whereas short-term inefficiencies still remain. The problem is giving a concrete shape to validate the existing beliefs about the short-term and long-term efficiencies or to disprove the conjecture.

Although the issue of market efficiency is a crucial one, and a lot of econometric and empirical research has been done on this topic (Fama, 1965; Fama and French, 1993; and Campbell et al., 1997), there is very little theoretical literature on it and no attempt has been made to formulate the problem mathematically or deal with it computationally. This paper attempts to define market efficiency rigorously and perform an analytical and numerical study of a simple model of trading. In particular, the questions that arise are: What is an optimal model for R&D in the financial market and what are the structural specifications of the stock market that help in gaining efficiency? Mukherjee and Ghosh (2006) have discussed the problem with regard to one financial asset. This paper generalizes it to two assets. A further generalization to multiple assets would be immediate, but algebraically tedious.

Financial Risk Management Journal, Financial Markets, Empirical Research, Theoretical Literature, Financial Assets, Bivariate Normal Expression, Bivariate Normal Density, Market Efficiency, Financial Asset Prices, Lognormal Distributions, Gaussian Estimation Strategy, Innovation Processes, Gaussian Price Exploration Algorithm.