23,309 research outputs found
Spanning Tests for Markowitz Stochastic Dominance
We derive properties of the cdf of random variables defined as saddle-type
points of real valued continuous stochastic processes. This facilitates the
derivation of the first-order asymptotic properties of tests for stochastic
spanning given some stochastic dominance relation. We define the concept of
Markowitz stochastic dominance spanning, and develop an analytical
representation of the spanning property. We construct a non-parametric test for
spanning based on subsampling, and derive its asymptotic exactness and
consistency. The spanning methodology determines whether introducing new
securities or relaxing investment constraints improves the investment
opportunity set of investors driven by Markowitz stochastic dominance. In an
application to standard data sets of historical stock market returns, we reject
market portfolio Markowitz efficiency as well as two-fund separation. Hence, we
find evidence that equity management through base assets can outperform the
market, for investors with Markowitz type preferences
Algorithm Portfolios for Noisy Optimization
Noisy optimization is the optimization of objective functions corrupted by
noise. A portfolio of solvers is a set of solvers equipped with an algorithm
selection tool for distributing the computational power among them. Portfolios
are widely and successfully used in combinatorial optimization. In this work,
we study portfolios of noisy optimization solvers. We obtain mathematically
proved performance (in the sense that the portfolio performs nearly as well as
the best of its solvers) by an ad hoc portfolio algorithm dedicated to noisy
optimization. A somehow surprising result is that it is better to compare
solvers with some lag, i.e., propose the current recommendation of best solver
based on their performance earlier in the run. An additional finding is a
principled method for distributing the computational power among solvers in the
portfolio.Comment: in Annals of Mathematics and Artificial Intelligence, Springer
Verlag, 201
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