Risk of Monetary Gambles: An Axiomatic Approach

Tomer Siedner

In this work we present five axioms for a risk-order relation defined over (monetary) gambles. We then characterize an index that satisfies all these axioms – the probability of losing money in a gamble multiplied by the expected value of such an outcome – and prove its uniqueness. We propose to use this function as the risk of a gamble. This index is continuous, homogeneous, monotonic with respect to first- and second-order stochastic dominance, and simple to calculate. We also compare our index with some other risk indices mentioned in the literature.

April, 2015