By Ewald C.-O.
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Additional resources for Discrete time finance
9. A financial market model is called complete, if for any contingent claim X there exists a replicating strategy (x, φ). A model which is not complete is called incomplete. 3 the issue of computing prices in complete market models is completely solved. But how to recognize complete models ? The following proposition gives us a criterion for completeness. 5. , ωk } is arbitrage free. e. rank(A) = k. Proof. By standard linear algebra the matrix A has full rank, if and only if for every X ∈ Rk the equation AZ = X has a solution Z ∈ Rn+1 .
A financial market model is called complete, if for any contingent claim X there exists a replicating strategy (x, φ). A model which is not complete is called incomplete. 3 the issue of computing prices in complete market models is completely solved. But how to recognize complete models ? The following proposition gives us a criterion for completeness. 5. , ωk } is arbitrage free. e. rank(A) = k. Proof. By standard linear algebra the matrix A has full rank, if and only if for every X ∈ Rk the equation AZ = X has a solution Z ∈ Rn+1 .
We will later consider the same question in more advanced models. e. what is our measure for the performance of a trading strategy. In order to define such a performance measure three fundamental characteristics of financial markets, or more precisely of the agents trading on the market, have to be included : 37 1. Agents prefer higher payoffs to less payoffs This idea is so innate to financial markets, that it doesn’t need any discussion. However we cannot judge trading strategies purely by this characteristic.