Arbitrage Theorem and its Applications

Tamás Nagy ()
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Tamás Nagy: University of Miskolc

Theory Methodology Practice (TMP), 2002, vol. 1, issue 01, 27-32

Abstract: In my article I describe the concept of financial rate of return and the value of return in a very simple model first. Then as generalisation of the model we take an experiment, which has n possible outcomes. We have the same m kind betting possibilities for each outcome. The financial rate of return is known for each outcome and betting possibility. We define the concept of arbitrage (the possibility of sure winning), and we are looking for the answer how to characterise the arbitrage exemption. What is the guarantee, that any betting terms cannot be given for which the winning is sure for each outcome? For this question the answer is given in the arbitrage theorem, which is one of the alternatives of the well-known Farkas theory. In the second part of the article I demonstrate some applications of the theorem. I apply it for a classical betting problem first, then for an option pricing in more details. The applications for the one-period binomial and trinomial, and the more-period binomial option pricing will also be made known.

Date: 2002
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