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Stochastic moment problem and hedging of generalized Black-Scholes options. (English) Zbl 1228.91074
Summary: In mathematical finance one is interested in the quadratic error which occurs while replacing a continuously adjusted portfolio by a discretely adjusted one. We first study higher order approximations of stochastic integrals. Then we apply the results to quantify quadratic error which occurs in estimating the discretely adjusted hedging risk in pricing European options in a generalized Black-Scholes market.

MSC:
91G60 Numerical methods (including Monte Carlo methods)
65D05 Numerical interpolation
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
91G20 Derivative securities (option pricing, hedging, etc.)
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