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Variance-optimal hedging in discrete time. (English) Zbl 0835.90008

Summary: We solve the problem of approximating in \({\mathcal L}^2\) a given random variable \(H\) by stochastic integrals \(G_T(\vartheta)\) of a given diskrete-time process \(X\). We interpret \(H\) as a contingent claim to be paid out at time \(T\), \(X\) as the price evolution of some risky asset in a financial market, and \(G(\vartheta)\) as the cumulative gains from trade using the hedging strategy \(\vartheta\). As an application, we determine the variance-optimal strategy which minimizes the variance of the net loss \(H-G_T(\vartheta)\) over all strategies \(\vartheta\).

MSC:

91B28 Finance etc. (MSC2000)
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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