5 Hedging jump-diffusion market models
In the previous section we have seen that, as a consequence of its incompleteness, in a jump-diffusion market model we have in general infinitely many martingale measures. We have then investigated the method of market completion as a tool to obtain a unique martingale measure. On the other hand, from the second fundamental theorem of asset pricing one has that, in general, if a market admits a unique equivalent martingale measure, then it is also complete in the sense that every contingent claim can be hedged by a self financing portfolio.
We shall investigate the hedging problem in a jump-diffusion market model having in mind two goals: for the first goal, in the context of asset price models, we shall show ...
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