Analyzing the Fundamental Theorem of Asset Pricing with Special Reference to African Stock Markets
Posted: 25 Mar 2019
Date Written: March 1, 2019
Abstract
The fundamental theorem of asset pricing is one of the most remarkable results in financial mathematics. Indeed in financial mathematics, asset pricing processes are modeled as stochastic processes on a given probability space (;F; P). In this project we discuss the fundamental theorem of asset pricing which relates the existence of an equivalent martingale measure to the no-arbitrage condition (i.e it is impossible to make money out of nothing) and states that a financial securities market model is arbitrage free if and only if there is a measure Q which is equivalent to the given measure P, under which all (discounted) asset price processes are martingale. We give an example of pricing, the mathematical and financial object useful for the main notions of this theorem and we provide a complete proof of this theorem for a discrete-time model with only nitely many states and nite horizon. The story of this theorem started - like most of modern Mathematical Finance with the work of F. Black, M. Scholes (1973:637) and R. Merton (1973:141). This is paper is a summary of a Master dissertation at the African Institute for Mathematical Sciences (AIMS) in South Africa.
Keywords: Theorem of Asset Pricing, African stock markets
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