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Optimal Approximations (optimal + approximation)

Distribution by Scientific Domains
Business, Economics, Finance and Accounting75%

Selected Abstracts

The Band Pass Filter*

INTERNATIONAL ECONOMIC REVIEW, Issue 2 2003
Lawrence J. Christiano
We develop optimal finite-sample approximations for the band pass filter. These approximations include one-sided filters that can be used in real time. Optimal approximations depend upon the details of the time series representation that generates the data. Fortunately, for U.S. macroeconomic data, getting the details exactly right is not crucial. A simple approach, based on the generally false assumption that the data are generated by a random walk, is nearly optimal. We use the tools discussed here to document a new fact: There has been a significant shift in the money,inflation relationship before and after 1960. [source]

Optimal approximations of nonlinear payoffs in static replication,

THE JOURNAL OF FUTURES MARKETS, Issue 11 2010
Qiang Liu
Static replication of nonlinear payoffs by line segments (or equivalently vanilla options) is an important hedging method, which unfortunately is only an approximation. If the strike prices of options are adjustable (for OTC options), two optimal approximations can be defined for replication by piecewise chords. The first is a naive minimum area approach, which seeks a set of strike prices to minimize the area enclosed by the payoff curve and the chords. The second improves on the first by taking the conditional distribution of the underlying into consideration, and minimizes the expected area instead. When the strike prices are fixed (for exchange-traded options), a third or the approach of least expected squares locates the minimum for the expected sum of squared differences between the payoff and the replicating portfolio, by varying the weights or quantities of the options used in the replication. For a payoff of variance swap, minimum expected area and least expected squares are found to produce the best numerical results in terms of cost of replication. Finally, piecewise tangents can also be utilized in static replication, which together with replication by chords, forms a pair of lower or upper bound to a nonlinear payoff. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark [source]

A two-grid method for expanded mixed finite-element solution of semilinear reaction,diffusion equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003
Yanping Chen
Abstract We present a scheme for solving two-dimensional semilinear reaction,diffusion equations using an expanded mixed finite element method. To linearize the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method. The solution of a non-linear system on the fine space is reduced to the solution of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h1/3). As a result, solving such a large class of non-linear equation will not be much more difficult than solving one single linearized equation. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Optimal approximations of nonlinear payoffs in static replication,

THE JOURNAL OF FUTURES MARKETS, Issue 11 2010
Qiang Liu
Static replication of nonlinear payoffs by line segments (or equivalently vanilla options) is an important hedging method, which unfortunately is only an approximation. If the strike prices of options are adjustable (for OTC options), two optimal approximations can be defined for replication by piecewise chords. The first is a naive minimum area approach, which seeks a set of strike prices to minimize the area enclosed by the payoff curve and the chords. The second improves on the first by taking the conditional distribution of the underlying into consideration, and minimizes the expected area instead. When the strike prices are fixed (for exchange-traded options), a third or the approach of least expected squares locates the minimum for the expected sum of squared differences between the payoff and the replicating portfolio, by varying the weights or quantities of the options used in the replication. For a payoff of variance swap, minimum expected area and least expected squares are found to produce the best numerical results in terms of cost of replication. Finally, piecewise tangents can also be utilized in static replication, which together with replication by chords, forms a pair of lower or upper bound to a nonlinear payoff. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark [source]