Saddle-Type Functionals for Continuous Processes with Applications to Tests for Stochastic Spanning
Stelios Stelios Arvanitis
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Stelios Stelios Arvanitis: Athens University of Economics and Business
No 201509, Working Papers from Athens University Of Economics and Business, Department of Economics
We derive the continuity properties of the cdf of a random variable deâined as a saddle-type point of a real valued continuous stochastic process on a compact metric space. This result facilitates the deri- vation of âirst order asymptotic properties of tests for stochastic spanning w.r.t. some stochastic domi- nance relation based on subsampling. As an illustration we define the concept of Markowitz stochastic span- ning, derive an analytic representation upon the empirical analog of which we construct a relevant statisti- cal test. The aforementioned result enables derivation of asymptotic exactness for the relevant procedure based on subsampling,when the metric space has the form of a simplicial complex, the spanning set is a compact subset and the signiâicance level is chosen according to the number of extreme points of the complex inside the spanning set. Consistency is also derived. Such tests are of interest in financial economics since they can provide reductions of portfolio sets.
Keywords: Continuous Process; Malliavin Derivative; Nested Optimizations; Saddle-Type Point; ConnectedSupport; Atom; AbsoluteContinuity; MarkowitzStochasticDominance; Stochastic Spanning; Spanning Test; Subsampling; Gaussian Process; Brownian Bridge; Asymptotic Exactness; Consistency. (search for similar items in EconPapers)
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