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Seminar on Probability and Statistics |
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Seminar on Probability and Statistics Friday May 11 2012 Tokyo 006 2:50-4:00 pm
Efficient Discretization of Stochastic Integrals
深澤 正彰 / FUKASAWA, Masaaki 大阪大学大学院理学研究科数学教室 / Department of Mathematics, Osaka University Abstract Sharp asymptotic lower bounds of the expected quadratic variation of
discretization error in stochastic integration are given. The theory
relies on inequalities for the kurtosis and skewness of a general
random variable which are themselves seemingly new. Asymptotically
efficient schemes which attain the lower bounds are constructed
explicitly. The result is directly applicable to practical hedging
problem in mathematical finance; it gives an asymptotically optimal
way to choose rebalancing dates and portofolios with respect to
transaction costs. The asymptotically efficient strategies in fact
reflect the structure of transaction costs. In particular a specific
biased rebalancing scheme is shown to be superior to unbiased schemes
if transaction costs follow a convex model. The problem is discussed
also in terms of the exponential utility maximization.
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