Financial Theory with Python

Chapter 5. Static Economy

A securities market model is viable if and only if there exists at least one equivalent martingale measure for it.

Harrison and Kreps (1979)

The central piece of the theory relating the no-arbitrage arguments with martingale theory is the so-called Fundamental Theorem of Asset Pricing.

Delbaen and Schachermayer (2006)

This chapter introduces more formalism to model a general static economy. Such an economy is characterized by an arbitrarily large, but still finite, state space. As before, the general static economy is analyzed at two relevant points in time only, for example, today and one year from now. Therefore, this chapter introduces one major generalization—namely with regard to the state space. The next chapter then generalizes the model economy further with regard to the number of relevant points in time. This enables one to also model dynamics.

The chapter makes use, as before, of linear algebra and probability theoretical concepts. Books that cover these topics well for the purposes of this chapter are Aleskerov et al. (2011) for linear algebra and Jacod and Protter (2004) for probability theory. A gentle introduction to general static economies and their analysis is found in Milne (1995). Pliska (1997) is a good introductory textbook on the topic that is both accessible and rigorous. Duffie (1988) is an advanced text that covers general static economies in greater detail, providing all the necessary tools from linear algebra and probability ...