This chapter addresses models that incorporate more than one kind of variability, variously called mixed, multilevel, multistratum, or hierarchical models. It starts by considering data with (1) changing amounts of variability or (2) correlation among data points. These kinds of data can be modeled adequately with the tools introduced in previous chapters. The last part of the chapter considers...

We consider a mean-variance hedging (MVH) problem for an arbitrage-free large financial market, i.e. a financial market with countably many risky assets modelled by a sequence of continuous semimartingales. By using the stochastic integration theory for a sequence of semimartingales developed in De Donno and Pratelli (2003), we extend the results about change of numéraire and MVH of Gourieroux,...

We have established a compact and transportable I2-stabilized Nd:YAG laser for international comparisons of laser frequency. The root Allan variance of the portable laser has reached 3 9 10 14 when the integration time is longer than 200 s. The results of an international comparison between the National Research Laboratory of Metrology (NRLM), Tsukuba, Japan and the JILA (formerly the Joint Ins...

We present results for the strangeness contribution to the nucleon, 〈N|s̄s|N〉 and to the spin of the nucleon, ∆s. By combining several variance reduction techniques for all-to-all propagators we are able to obtain gains in terms of computer time of factors of 25–30 for the disconnected loop that is needed within the calculation of ∆s, relative to the standard approach of just employing time part...

We introduce a new version of Stein’s method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance has to be bounded has an explicit formula that makes it possible to carry out the program more easily. As an applicatio...

We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure P ⋆ which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to P ⋆ coincides with the variance-optimal martin-gale measure relative to the original probability measure P .