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| Abstract |
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The classical question in quantitative finance is to provide pricing operators for derivative securities that are in some sense consistent with the observed market prices. Another classical study is to provide hedging strategies. In fact, these two questions are in duality and are always solved together.
Indeed, in the classical theories one assumes an underlying "historical" probability measure and all inequalities are understood almost-surely with respect to this measure.
In this structure, the classical fundamental theorem of asset pricing (FTAP) states that under the assumption of generalized no-arbitrage, there are risk neutral probability measures which provide linear pricing rules. FTAP proves not only the equivalence between no-arbitrage and the existence of such measures but also shows that these measures are the only possible ones.
In these talks, we consider a more general financial market with Knightian uncertainty. Although in such markets - by definition - there is no historical measure, the basic duality between hedging and pricing still holds. We illustrate this connection by several convex duality results starting with simple discrete time models. |
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