Subjective Expected Utility with Non-Increasing Risk Aversion

It is shown that assumptions about risk aversion, usually studied under the pre-supposition of expected utility maximization, have a surprising extra merit at an earlier stage of the measurement work: together with the sure-thing principle, these assumptions imply subjective expected utility maximization for monotonic continuous weak orders

On the relaxation of integral functionals depending on the symmetrized gradient

We prove results on the relaxation and weak* lower semicontinuity of integral functionals of the form $$\mathcal{F}[u] := \int_{\Omega} f \bigg( \frac{1}{2} \bigl( \nabla u(x) + \nabla u(x)^T \bigr) \bigg)\,\mathrm{d} x, \qquad u : \Omega \subset \mathbb{R}^d \to \mathbb{R}^d,$$ over the space $\mathrm{BD}(\Omega)$ of functions of bounded deformation or over the Temam-Strang space $$\mathrm{U}(\Omega):=\bigl\{u\in \mathrm{BD}(\Omega): \ \mathrm{div} \ u\in \mathrm{L}^2(\Omega)\bigr\},$$ depending on the growth and shape of the integrand $f$. Such functionals are interesting for example in the study of Hencky plasticity and related models.Comment: 30 page

Least Concave Ordinal Utility Function and the Marshalian Cardinal Utility

This paper examines the conditions under which the Marshallian type of cardinal utility function can be derived from a class of ordinal utility functions

Economic Theory in the Mathematical Mode

Lecture to the memory of Alfred Nobel, December 8, 1983general equilibrium;

Learning Theory and Algorithms for Revenue Optimization in Second-Price Auctions with Reserve

Second-price auctions with reserve play a critical role for modern search engine and popular online sites since the revenue of these companies often directly de- pends on the outcome of such auctions. The choice of the reserve price is the main mechanism through which the auction revenue can be influenced in these electronic markets. We cast the problem of selecting the reserve price to optimize revenue as a learning problem and present a full theoretical analysis dealing with the complex properties of the corresponding loss function. We further give novel algorithms for solving this problem and report the results of several experiments in both synthetic and real data demonstrating their effectiveness.Comment: Accepted at ICML 201