Profesional competentes valuation and trainer functions

Sketching valuation functions

Motivated by the problem of querying and communicating bidders’ valuations in combinatorial auctions, we study how well different classes of set functions can be sketched. More formally, let f be a function mapping subsets of some ground set [n] to the non-negative real numbers. We say that f ′ is an α-sketch of f if for every set S, the value f ′(S) lies between f(S)/α and f(S), and f ′ can be...

Learning Valuation Functions

A core element of microeconomics and game theory is that consumers have valuation functions over bundles of goods and that these valuation functions drive their purchases. In particular, the value assigned to a bundle need not be the sum of values on the individual items but rather is often a more complex function of how the items relate. The literature considers a hierarchy of valuation classe...

Analytical Ramifications of Derivatives Valuation: Asian Options and Special Functions

Averaging problems are ubiquitous in Finance with the valuation of the so–called Asian options on arithmetic averages as their most conspicuous form. There is an abundance of numerical work on them, and their stochastic structure has been extensively studied by Yor and his school. However, the analytical structure of these problems is largely unstudied. Our philosophy now is that such valuation...

Testing Submodularity and Other Properties of Valuation Functions

We show that for any constant ǫ > 0 and p ≥ 1, it is possible to distinguish functions f : {0, 1} → [0, 1] that are submodular from those that are ǫ-far from every submodular function in lp distance with a constant number of queries. More generally, we extend the testing-by-implicit-learning framework of Diakonikolas et al. (2007) to show that every property of real-valued functions that is wel...

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