评罗伯特·奥曼及其博弈理论——冲突与合作

杰出的经济学家罗伯特.奥曼在决策制定理论方面取得的辉煌成就,对博弈论和其他一些相关经济理论的形成和发展起到了不可或缺的作用。其博弈理论涉及到现代博弈论最重要、最基本的核心问题,为博弈论的发展开辟了许多新的领域和思路。目前,现代经济生活中的冲突与合作主要表现为“刷卡风波”,商家认为在利润率不高,顾客刷卡率上升的情况下,银行的刷卡收费率太高,商家已不堪重负。根据奥曼的合作博弈理论和重复博弈理论,银商矛盾的最终化解在于银商双方通过博弈寻求合作,应考虑我国的具体情况,出台商户刷卡相关优惠政策,探讨银行、商户、顾客三方共赢的新模式。     

Bayesian beliefs with stochastic monotonicity: An extension of Machina and Schmeidler

Machina and Schmeidler show that the probabilistic sophistication can be obtained in an Anscombe–Aumann setting without imposing expected utility by maintaining stochastic monotonicity and adding a new axiom loosely analogous to Savage's P4. This analogous axiom, however, is very strong. In this note, we obtain probabilistic sophistication using a weaker (and more natural) analog of Savage's P4. Stochastic monotonicity is sufficient to bridge the gap, where Anscombe and Aumman use independence twice, we use stochastic monotonicity twice.     

Random Sets: Models and Statistics

This paper surveys aspects of the theory of random closed sets, focussing on issues of practical and current interest. First, some historical remarks on this part of probability theory are made, where the important role of Georges Matheron is emphasized. Then, fundamental characteristics of the distribution of random closed sets are introduced. The very important Boolean model serves as an example for discussing mathematical and statistical problems. A number of further models is then considered, namely excursion sets of random fields, the system of edges of the Poisson Voronoi tessellation and various random systems of non-overlapping spheres. Finally, some ideas of particle statistics are presented, including some models of random compact sets.     

Evaluation by the Aumann and Serrano performance index and Sharpe ratio: Bitcoin performance

We compare Bitcoin performance based on the Aumann and Serrano performance index and Sharpe ratio assuming that asset returns follow the class of discrete normal mixture distributions. The Aumann and Serrano performance index can take into account higher moments of the underlying distribution of assets and is relevant for risk-averse investors. We evaluate Bitcoin performance based on the Aumann and Serrano index relative to the performance of other assets. Our evaluation shows that Bitcoin is rated highly by the Sharpe ratio but rated very poorly by the Aumann and Serrano index. We also find some stock assets can beat Bitcoin by the Sharpe ratio when an investment horizon is monthly.     

Temporal aggregation of the Aumann–Serrano and Foster–Hart performance indexes

We investigate the temporal aggregation of the Aumann–Serrano (AS) and Foster–Hart (FH) performance indexes considered by Kadan and Liu (2014). We provide sufficient conditions for the two indexes to be closed under temporal aggregation, that is, for the two indexes to have the same values when the observations are aggregated. Here, we present empirical examples using U.S. stock data and the four anomalies studied by Fama and French (1993) and Carhart (1997), where the two indexes have nearly identical values in some stocks and one anomaly when the observations are aggregated. Unlike the Sharpe ratio, the AS and FH performance indexes have more stable properties with respect to temporal aggregation.