A kind of stochastic recursive Zero-Sum differential game problem with double obstacles constraint

Abstract

This paper concerns a class of stochastic recursive zero-sum differential game problem with recursive utility related to a backward stochastic differential equation (BSDE) with double obstacles. A sufficient condition is provided to obtain the saddle-point strategy under some assumptions. In virtue of the corresponding relationship of doubly reflected BSDE and mixed game problem, a stochastic linear recursive mixed differential game problem is studied to apply our theoretical result, and here the explicit saddle-point strategy as well as the saddle-point stopping time for the mixed game problem are obtained. Besides, a numeral example is also given to demonstrate the result by virtue of partial differential equations (PDEs) computation method.     

Expected utility, μ-σ preferences,and linear distribution classes: A further result

This article is an extension of Meyer and Sinn's results on the representation of arbitrary von Neumann-Morgenstern functions in - space when the probability distributions to be compared belong to a linear distribution class. It shows that, when absolute risk aversion decreases, stays constant, or increases not too fast, an increase in , given , increases the indifference curve slope: increased riskiness increases the required marginal compensation for risk when risk is measured by the standard deviation of wealth or income.I gratefully acknowledge useful comments by Wolfgang Buchholz, Kai Konrad, Jack Meyer, Hans Schneeweiß, Dominique Thon, and Bengt Arne Wickström.     

The Becker-DeGroot-Marschak mechanism and nonexpected utility: A testable approach

The Becker-DeGroot-Marschak mechanism is widely used to elicit decision makers' selling prices of lotteries. This mechanism leads, however, to the preference reversal phenomenon, which seemed to indicate nontransitive preferences. To solve this puzzle, Karni and Safra (1987) introduced a new interpretation of this mechanism based on two-stage lotteries without the independence axiom. In this article, we suggest a set of empirically testable hypotheses based on their interpretation of the mechanism. One of these tests can be used to find the utility and the probability transformation functions of an anticipated utility maximizer.This article consists of an earlier paper with a similar title (University of Toronto WP #8809) and the paper Elicitation of Certainty Equivalents and the Becker-DeGroot-Marschak Mechanism.     

A Proportional Random Utility Approach to Qualitative Response Models

A new functional form of the response probability for a qualitative response model is proposed. The new model is flexible enough to avoid the constraint of independence from irrelevant alternatives, which is perceived as a weakness of the multinomial logit model in some applications. It is computationally simpler than the multinomial probit model and is promising for analyzing problems with a moderate number of alternatives.     

Some asymptotic properties of point estimation with n-dimensional fuzzy data

Some asymptotic properties of point estimation with n-dimensional fuzzy data with respect to a special L ₂-metric ρ are investigated in this article. It is shown that the collection of all n-dimensional fuzzy data endowed with the ρ-metric is a complete and separable space. Some criterions for point estimation in such fuzzy environments are proposed, and the sample mean, variance and covariance with n-dimensional fuzzy data under these criteria are further studied.     

Testing the homogeneous marginal utility of income assumption

We develop a test for the hypothesis that every agent from a population of heterogeneous consumers has the same marginal utility of income function. This homogeneous marginal utility of income (HMUI) assumption is often (implicitly) used in applied demand studies because it has nice aggregation properties and facilitates welfare analysis. If the HMUI assumption holds, we can also identify the common marginal utility of income function. We apply our results using a U.S. cross sectional dataset on food consumption.     

童心与佛理契合的世界--丰子恺审美理想解读

真诚的人性与和平的生活环境对于丰子恺追求率真自然的童心有着重要的影响.这种深刻的童年经验构成了他摒弃功利、标举情感的审美观.对万事无常的朦胧体悟又使他与佛教有种自然的亲近.质朴无华的童心是丰子恺追求的自然境界,仁爱超脱的佛理则是他景仰的天地境界.丰子恺的审美理想就表现为童心与佛理的契合之间.     

Ranked-Weighted Utilities and Qualitative Convolution

For gambles—non-numerical consequences attached to uncertain chance events—analogues are proposed for the sum of independent random variables and their convolution. Joint receipt of gambles is the analogue of the sum of random variables. Because it has no unique expansion as a first-order gamble analogous to convolution, a definition of qualitative convolution is proposed. Assuming ranked, weighted-utility representations (RWU) over gains (and, separately, over losses, but not mixtures of both), conditions are given for the equivalence of joint receipt, qualitative convolution, and a utility expression like expected value. As background, some properties of RWU are developed.     

Lifetime Uncertainty and Time Preference

Despite Fisher's (1930) psychological intuitions of and the formal treatment given by Yaari (1965, Review of Economic Studies 32, 137), the intertemporal model of choice is mainly a model with certain lifetime. The purpose of this paper is to reconsider this assumption, starting from a very simple two-period model of choice with lifetime uncertainty. We examine the comparative statics of the model at the first two orders and replace the concept of `pure time preference' by taking into account the subjective treatment of the probability of survival. This revised version was published online in June 2006 with corrections to the Cover Date.     

Additive time-dependent hazard model with doubly truncated data

For doubly truncated data, i.e. the variables of interest are only observable if they lie in a certain random interval, an additive hazard model with time-dependent regression coefficients is investigated. Consistency and asymptotic normality are proven under mild assumptions. A simulation study investigates the finite sample properties and the influence of the truncation distribution on the estimation error. Finally, the method is applied to a doubly truncated data set of German companies, where the age at insolvency is of interest.