Two-Dimensional Risk-Neutral Valuation Relationships for the Pricing of Options.

The Black-Scholes model is based on a one-parameter pricing kernel with constant elasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel with at least two parameters. We price European-style options on assets whose probability distributions have two unknown parameters. We assume a pricing kernel which also has two unknown parameters. When certain conditions are met, a two-dimensional risk-neutral valuation relationship exists for the pricing of these options: i.e. the relationship between the price of the option and the prices of the underlying asset and one other option on the asset is the same as it would be under risk neutrality. In this class of models, the price of the underlying asset and that of one other option take the place of the unknown parameters.

The utility premium of Friedman and Savage, comparative risk aversion, and comparative prudence

We show that the utility premium of Friedman and Savage can be used to explain comparative risk aversion and comparative prudence. More precisely, we show that the greater the risk aversion measure, the greater a risk's utility premium normalized by the marginal utility and that the greater the prudence measure, the greater the utility premium for disaggregating a certain loss of wealth and a zero-mean risk normalized by the utility function's second derivative

Cautiousness in the small and in the large

We characterize cautiousness, a downside risk aversion measure, using a simple portfolio problem in which agents invest in a stock, a risk-free bond, and an option on the stock. We present two different characterizations by answering the following two questions respectively: who buys the option? who buys more options per share of the stock? Our characterizations use a strong notion of an increase in skewness defined by Van Zwet (1964)

Keeping Business Education Relevant: A Contextual Curriculum to Sustain Secondary Business Education Programs

The future of secondary business education is being threatened by increased educational reform and changes in student interests that coincide with changes in the labor market. From 1982 to 1998 the percentage of high school students earning three credits or more in business education has decreased by nearly 60%. It is clear that students are not interested in the courses that make up traditional business education. High school students have shown a dramatic interest in entrepreneurship. Entrepreneurship has also been recognized as an excellent contextual framework from which business academic subject matter can be learned. Contextual learning increases academic achievement which is a focal point of reform in vocational and career education. A tremendous opportunity exists for secondary business education curriculum developers to design an integrated contextual curriculum that addresses reform challenges and revitalizes student interests

Livestock health priorities in the Tanzania livestock master plan

Bill & Melinda Gates Foundatio

Dairy development in the Tanzanian Livestock master plan

Bill & Melinda Gates Foundatio

Red meat production in the Tanzanian livestock master plan

Bill & Melinda Gates Foundatio

Pork production in the Tanzanian livestock master plan

Bill & Melinda Gates Foundatio

Institutions and policies to implement the Tanzania livestock master plan

Bill & Melinda Gates Foundatio