"Search under the Knightian Uncertainty"

Suppose that "uncertainty" about labor market conditions has increased. Does this change induce an unemployed worker to search longer, or shorter? This paper shows that the answer is drastically different depending on whether an increase in "uncertainty" is an increase in risk or that in true uncertainty in the sense of Frank Knight. We show in a general framework that, while an increase in risk (the mean-preserving spread of the wage distribution that the worker thinks she faces) increases the reservation wage, an increase in the Knightian uncertainty (a decrease in her confidence about the wage distribution) reduces it.

"Economics of Self-Feeding Fear"

A model of self-feeding fear is presented. Suppose that an economic agent is (1-ƒÃ)~100% certain that uncertainty she faces is characterized by a particular probability measure, but that she has a fear that, with ƒÃ~100% chance, her conviction is completely wrong and she is left perfectly ignorant about the true measure in the present as well as in the future. We call this situation ƒÃ-contamination of confidence. In this situation, if the economic agent follows Bayesian procedure or its variant, which is considered as rational in the theory of economics, her confidence erodes after having new observation.

"Liquidity Motives of Holding Money under Investment Risk: A Dynamic Analysis"

Jones and Ostroy (1984) argue that money,as an asset of the least transaction cost, offers exibility to its holder, which other assets cannot provide. We extend the idea of Jones and Ostroy into a truely dynamic framework of infinite horizon with a risk-neutral decision-maker. We then investigate the effect of an increase in investment risk on the demand for liquidity a la Jones and Ostroy. In particular, we prove that the opitmal strategy exists, that it has a reservation property, and that the reservation value increases when investment risk increases in the sense of a mean-preserving spread. While the effect of a mean-preserving spread on the reservation value is unambiguous, its e ect on money demand is ambiguous. We then provide conditions on increasing investment risk under which money demand unambiguously increases.

"A Simple Axiomatization of Iterated Choquet Objectives"

A set of axioms which characterizes a preference representable by the iterated Choquet expected utility is presented. This objective function is attractive since it possesses a feature of dynamical consistency. Furthermore,we show that under the same axioms the conditional preference is represented by the Choquet expected utility with respect to the capacity which is updated according to the Dempster-Shafer rule. We do this by weakening Schmeidler's axiom of comonotonic independence to our axiom of constrained comonotonic independence and by adding the axiom of dynamical consistency.

"An Axiomatic Approach to ƒÃ-contamination"

Suppose that an economic agent is (1|ƒÃ)~100% certain that uncertainty she faces is characterized by a particular probability measure, but that she has a fear that, with ƒÃ~100% chance, her conviction is completely wrong and she is left perfectly ignorant about the true measure in the present as well as in the future.This situation is often called "ƒÃ-contamination of con dence." The purpose of this paper is to provide a simple set of behavioral axioms under which the decision-maker's preference is represented by the Choquet expected utility with the ƒÃ-contamination of con dence.

"Irreversible Investment and Knightian Uncertainty"

When firms decide about irreversible investment, they may not have perfect confidence about their perceived probability measure describing future uncertainty. They may think other probability measures perturbed from the original one are also probable. Uncertainty characterized by not a single probability measure but a set of probability measures is called Knightian uncertainty. The effect of Knightian uncertainty on the value of irreversible investment opportunity is shown to be drastically different from that of the traditional uncertainty in the form of risk. Specifically, an increase in Knightian uncertainty decreases the value of investment opportunity while an increase in risk increases it.

"A Note on Learning under the Knightian Uncertainty"

In contrast to the traditional model of uncertainty, where the uncertainty is characterized by a single distribution function that a decision maker faces, the Knightian-uncertainty approach characterizes it as a set of distributions rather than a single one. Hence, learning in the context of Knightian uncertainty is characterized by an update process of the set of distributions after each of random sampling. This note presents two examples in which the Dempster-Shafer update rule, the one which attracts much attention since it seems intuitive, does not at all reduce the Knightian uncertainty (Example 1) and it actually increases the Knightian uncertainty (Example 2). Thus, what is a sensible update process is still an open question under the Knightian uncertainty.

A Renewal Process Model for Use in Seismic Risk Analysis

A model of random occurrence of earthquakes using a renewal process is proposed on the basis of the catalogue of historical earthquakes for Kyoto, Japan. The model accounts for the variation of annual occurrence rate depending on the intervals between successive earthquakes. It can incorporate widely recognized nonstationary features of earthquake occurrences that can not be explained with the conventional simple Poisson process models. By using the renewal process model, called herein the double Poisson process model, one can estimate the probability of future earthquake occurrences in terms of the conditional probability based on the time since the last earthquake. Numerical results are presented for the Kyoto area