Choosing Investment Strategies by their Outcomes

Sharpe has shaped recent thinking in the financial sciences with his paper on the Distribution Builder, a tool designed to elicit investor preferences as probability distributions. We examine pricing such distributions in simple financial models. The no-arbitrage pricing method is a well studied technique for pricing derivative securities in financial market models. We apply this method to price arbitrary probability distributions on finite outcome spaces. This work surfaces constraints on the technique as the number of possible investment outcomes increases, and examines these constraints from multiple perspectives