Pricing insurance risk is a book I am writing with John Major. It describes the last mile of underwriting. Actuaries and accountants have determined the cost of goods sold: the expected loss cost, direct and allocated expenses. In fact they have gone beyond simple point estimates and have provided a full range of potential outcomes, understood within the context of all the other risks written by the company. All that remains is to set a manual rate or quote a price or to accept or reject an offered market price (firm order). The book will describe the actuarial, risk theory, finance and accouning approaches to pricing insurance risk.
When does it make sense for different risks to pool together? This paper investigates equilibrium risk pools in a market with risk-based solvency regulation and costly capital. It considers a market with two classes of risk, each having different aggregate volatility characteristics, such as personal auto and catastrophe exposed property. It identifies three possible equilibrium solutions: a single multiline pool, a multiline pool and a monoline pool, and two monoline pools. The results help explain various features seen in insurance markets, including the structure of the Florida homeowners market and the US medical malpractice market, and it can be applied more broadly to any regulated risk market.
We introduce a straightforward algorithm to determine a range of prices consistent with complete information about the risk but only partial information about the pricing risk measure. In many cases the algorithm produces bounds tight enough to be useful in practice. We illustrate the theory by applying it to three important problems: pricing for high limits relative to low limits, evaluating reinsurance programs, and portfolio-level strategic decision making. We also show how the theory can be used to test if prices for known risks are consistent with a single partially specified risk measure.