Heterogeneous Risk Attitudes in a Continuous-Time Model

We prove that every continuous-time model in which all consumers have time-homogeneous and time-additive utility functions and share a common probabilistic belief and a common discount rate can be reduced to a static model. This result allows us to extend some of the existing results on the representative consumer and risk-sharing rules in static models to continuous-time models. We show that the equilibrium interest rate is lower and more volatile than in the standard representative consumer economy, and that the individual consumption growth rates are more dispersed than is predicted from the first-order conditions.Heterogeneity, risk attitudes, hyperbolic absolute risk aversion, representative consumer, risk-sharing rules, mutual fund theorem, Ito's Lemma, interest rates.

On the foundations of Lévy finance: Equilibrium for a single-agent financial market with jumps

For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before, only flow consumption is allowed. The agent's utility function is assumed to be additive, defined via strictly increasing, strictly concave smooth felicity functions which are bounded below (thus, many CRRA and CARA utility functions are included). For technical reasons we require that only pathwise continuous trading strategies are permitted in the demand set. The resulting equilibrium prices depend on the agent's risk-aversion through the felicity functions. It turns out that these prices will be the (stochastic) exponential of a Lévy process essentially only if this process is geometric Brownian motion.financial equilibrium, asset pricing, representative agent models, Lévy processes, nonstandard analysis

On the support of the Ashtekar-Lewandowski measure

We show that the Ashtekar-Isham extension of the classical configuration space of Yang-Mills theories (i.e. the moduli space of connections) is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices. These results are then used to prove that the classical configuration space is contained in a zero measure subset of this extension with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure. Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the ``extended" configuration space.Comment: 22 pages, Tex, Preprint CGPG-94/3-

Quantum Algorithms for Some Hidden Shift Problems

Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structures of functions, especially periodicity. The fact that Fourier transforms can also be used to capture shift structure has received far less attention in the context of quantum computation. In this paper, we present three examples of "unknown shift" problems that can be solved efficiently on a quantum computer using the quantum Fourier transform. For one of these problems, the shifted Legendre symbol problem, we give evidence that the problem is hard to solve classically, by showing a reduction from breaking algebraically homomorphic cryptosystems. We also define the hidden coset problem, which generalizes the hidden shift problem and the hidden subgroup problem. This framework provides a unified way of viewing the ability of the Fourier transform to capture subgroup and shift structure

Evidence for an additive inhibitory component of contrast adaptation

The latency of visual responses generally decreases as contrast increases. Recording in the lateral geniculate nucleus (LGN), we find that response latency increases with increasing contrast in ON cells for some visual stimuli. We propose that this surprising latency trend can be explained if ON cells rest further from threshold at higher contrasts. Indeed, while contrast changes caused a combination of multiplicative gain change and additive shift in LGN cells, the additive shift predominated in ON cells. Modeling results supported this theory: the ON cell latency trend was found when the distance-to-threshold shifted with contrast, but not when distance-to-threshold was fixed across contrasts. In the model, latency also increases as surround-to-center ratios increase, which has been shown to occur at higher contrasts. We propose that higher-contrast full-field stimuli can evoke more surround inhibition, shifting the potential further from spiking threshold and thereby increasing response latency