Prospect and Markowitz Stochastic Dominance

Levy and Levy (2002, 2004) develop the Prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend Levy and Levy's Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Prospect theory has been regarded as a challenge to the expected utility paradigm. Levy and Levy (2002) prove that the second order PSD and MSD satisfy the expected utility paradigm. In our paper we take Levy and Levy's results one step further by showing that both PSD and MSD of any order are consistent with the expected utility paradigm. Furthermore, we formulate some other properties for the PSD and MSD including the hierarchy that exists in both PSD and MSD relationships; arbitrage opportunities that exist in the first orders of both PSD and MSD; and that for any two prospects under certain conditions, their third order MSD preference will be ???the opposite??? of or ???the same??? as their counterpart third order PSD preference. By extending Levy and Levy's work, we provide investors with more tools for empirical analysis, with which they can identify the first order PSD and MSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors to identify the third order PSD and MSD prospects and make better choices.Prospect stochastic dominance, Markowitz stochastic dominance, risk seeking, risk averse, S-shaped utility function, reverse S-shaped utility function

On the Estimation of Cost of Capital and its Reliability

Gordon and Shapiro (1956) first equated the price of a share with the present value of future dividends and derived the well-known relationship. Since then, there have been many improvements on the theory. For example, Thompson (1985, 1987) combined the "dividend yield plus growth" method with Box-Jenkins time series analysis of past dividend experience to estimate the cost of capital and its "reliability" for individual firms. Thompson and Wong (1991, 1996) proved the existence and uniqueness of the cost of capital and provided formula to estimate both the cost of capital and its reliability. However, their approaches cannot be used if the "reliability" does not exist or if there are multiple solutions for the "reliability". In this paper, we extend their theory by proving the existence and uniqueness of this reliability. In addition, we propose the estimators for the reliability and prove that the estimators converge to a true parameter. The estimation approach is further simplified, hence rendering computation easier. In addition, the properties of the cost of capital and its reliability will be analyzed with illustrations of several commonly used Box-Jenkins models.

GeneNotes – A novel information management software for biologists

BACKGROUND: Collecting and managing information is a challenging task in a genome-wide profiling research project. Most databases and online computational tools require a direct human involvement. Information and computational results are presented in various multimedia formats (e.g., text, image, PDF, word files, etc.), many of which cannot be automatically processed by computers in biologically meaningful ways. In addition, the quality of computational results is far from perfect and requires nontrivial manual examination. The timely selection, integration and interpretation of heterogeneous biological information still heavily rely on the sensibility of biologists. Biologists often feel overwhelmed by the huge amount of and the great diversity of distributed heterogeneous biological information. DESCRIPTION: We developed an information management application called GeneNotes. GeneNotes is the first application that allows users to collect and manage multimedia biological information about genes/ESTs. GeneNotes provides an integrated environment for users to surf the Internet, collect notes for genes/ESTs, and retrieve notes. GeneNotes is supported by a server that integrates gene annotations from many major databases (e.g., HGNC, MGI, etc.). GeneNotes uses the integrated gene annotations to (a) identify genes given various types of gene IDs (e.g., RefSeq ID, GenBank ID, etc.), and (b) provide quick views of genes. GeneNotes is free for academic usage. The program and the tutorials are available at: . CONCLUSIONS: GeneNotes provides a novel human-computer interface to assist researchers to collect and manage biological information. It also provides a platform for studying how users behave when they manipulate biological information. The results of such study can lead to innovation of more intelligent human-computer interfaces that greatly shorten the cycle of biology research