The effective (geometric mean) return of a periodically rebalanced portfolio always exceeds the weighted sum of the component geometric means. Some approximate formulae for estimating this effective return are derived and tested. One special case of these formulae is shown to be particularly...

In this note we investigate the Shapley value for fuzzy games proposed by Hwang and Liao (2009). We show that there exists a transferable-utility (TU) decomposition games that can be adopted to characterize the fuzzy Shapley value, i.e., the fuzzy Shapley value consists of the Shapley value of...

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance-covariance matrices, and the other is on offdiagonal sub-matrices which define the covariance between two non-overlapping segments of the high-dimensional...

Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance Σ , we propose a test for Σ being banded with possible diverging bandwidth. The test is adaptive to the “large p , small n ” situations without assuming a specific parametric distribution for...

We extend the finite automata approach to evaluate complexity of strategies in iterative adjustment processes such as auctions. Intuitively, a strategy's complexity is equal to the number of different contingencies in which qualitatively different behaviors are prescribed. Complexity may explain...

There is a surprising disconnect between formal rational choice theory and philosophical work on reasons. The one is silent on the role of reasons in rational choices, the other rarely engages with the formal models of decision problems used by social scientists. To bridge this gap, we propose a...

Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Instead, pref- erences are usually assumed to be �xed and exogenously given. Building on related work on reasons and rational choice (Dietrich...

Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It o¤ers few resources to describe some prior beliefs as rational or well-justi�ed, and...