431 research outputs found

    Favorable Classes of Lipschitz Continuous Functions in Subgradient Optimization

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    Clarke has given a robust definition of subgradients of arbitrary Lipschitz continuous functions f on R^n, but for purposes of minimization algorithms it seems essential that the subgradient multifunction partial f have additional properties, such as certain special kinds of semicontinuity, which are not automatic consequences of f being Lipschitz continuous. This paper explores properties of partial f that correspond to f being subdifferentially regular, another concept of Clarke's, and to f being a pointwise supremum of functions that are k times continuously differentiable

    Arbitrage and deflators in illiquid markets

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    This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with transaction costs or bid-ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. In the presence of nonlinearities, the classical notion of arbitrage turns out to have two equally meaningful generalizations, a marginal and a scalable one. We study their relations to state price deflators by analyzing two auxiliary market models describing the local and global behavior of the cost functions and constraints

    On the Interchange of Subdifferentiation and Conditional Expectation for Convex Functionals

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    We show that the operators E^G (conditional expectation given a tau-field G) and partial (subdifferentiation), when applied to a normal convex integrand f, commute if the effective domain multifunction omega -> {x E R^n | f(omega , x) < +infinity } is G-measurable
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