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In general, under an EMM, does there necessarily exist a replicating portfolio for every derivative?

I believe the answer to this is false. A simple example is a discrete time, trinomial model.

However:

In a complete market, i.e. the EMM is unique, does there necessarily exist a replicating portfolio for (at least all European) derivatives?

In the only 2 models I know - being Black-scholes and Binomial model, this is true, but is this true in general?

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This is known to be true in very wide generality. In the mathematical finance literature, it is often called the second fundamental theorem of asset pricing. The proof echoes, in some respects the martingale representation theorem. Intuitively, if there are some derivatives that cannot be hedged perfectly, there is some flexibility in arbitrage-free ways of pricing these derivatives, and this leads to the existence of multiple EMM's.

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but that says complete market iff unique EMM, but does unique EMM/completeness mean replication is possible? –  Lost1 Jan 8 at 23:38
    
Complete market is the same as replication, no? –  quasi Jan 8 at 23:40
    
right i see. maybe my question should have been 'what does it mean by a market is complete' –  Lost1 Jan 8 at 23:43

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