Variance-Optimal Hedging in Discrete Time

Martin Schweizer
1995 Mathematics of Operations Research  
We solve the problem of approximating in L 2 a given random variable H by stochastic integrals G T (ϑ) of a given discrete-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(ϑ) as the cumulative gains from trade using the hedging strategy ϑ. As an application, we determine the varianceoptimal strategy which minimizes the variance of the net loss H − G T (ϑ) over all strategies ϑ.
doi:10.1287/moor.20.1.1 fatcat:jyurnhzpdndgdmdtfj7mv2d5pe