Arbitrage Theorem and its Applications
Keywords:
Financial rate, Arbitrage theoremAbstract
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.
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