Some Applications of the Fundamental Theorem

1 Introduction

The theorem discussed in the previous chapter establishes important no-arbitrage conditions that permit pricing and risk management using Martingale methods. According to these conditions, given unique arbitrage-free state prices, we can obtain a synthetic probability measure, image, under which all asset prices normalized by a particular Zt become Martingales. Letting C(St, t) represent a security whose price depends on an underlying risk St, we can write,

image (1)

As long as positive ...

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