5,361 research outputs found
The exponentially convergent trapezoidal rule
It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators
Almost sure optimal hedging strategy
In this work, we study the optimal discretization error of stochastic
integrals, in the context of the hedging error in a multidimensional It\^{o}
model when the discrete rebalancing dates are stopping times. We investigate
the convergence, in an almost sure sense, of the renormalized quadratic
variation of the hedging error, for which we exhibit an asymptotic lower bound
for a large class of stopping time strategies. Moreover, we make explicit a
strategy which asymptotically attains this lower bound a.s. Remarkably, the
results hold under great generality on the payoff and the model. Our analysis
relies on new results enabling us to control a.s. processes, stochastic
integrals and related increments.Comment: Published in at http://dx.doi.org/10.1214/13-AAP959 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Analysis and application of minimum variance discrete time system identification
An on-line minimum variance parameter identifier was developed which embodies both accuracy and computational efficiency. The new formulation resulted in a linear estimation problem with both additive and multiplicative noise. The resulting filter is shown to utilize both the covariance of the parameter vector itself and the covariance of the error in identification. It is proven that the identification filter is mean square covergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm
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