Arbitrage Free Risk Loads For Brokers

When actuaries write about an insurance pricing formula, they first identify the formula in question and then discuss the pros and cons of it. This is in stark contrast to capital markets pricing papers, which start with a list of desirable axioms and then proceed by deriving the necessary and sufficient formula that satisfies these axioms. This paper follows the capital markets paradigm, deriving the necessary and sufficient risk load formula from a set of axioms that are uniquely appropriate for insurance. The derivation follows the same basic approach as Black-Scholes, but it differs in that the axioms have been re-selected to be descriptive of how an efficient insurance market operates. The result is a risk load formula commonly known as the Proportional Hazard Transform. This paper also provides an outline of how to implement the Proportional Hazard Transform, making it relevant and accessible to pricing actuaries.