Risk loading

Filip Lundberg set out in 1903, in his Uppsala thesis, the collective risk model from which ruin theory draws a classical result: a premium equal to expected loss leads to ruin with probability one over an infinite horizon. Surplus then follows a driftless walk, and a driftless walk hits zero. The risk loading is the drift you add. It pays for the capital the shareholder ties up to absorb deviations; its correct size therefore depends on the capital the risk consumes, and not on its expectation. Three calculation principles coexist and give different answers. A loading proportional to expectation is simple and blind to volatility, so it underprices dispersed risks. A loading proportional to standard deviation recognizes volatility but not dependence with the rest of the book. A cost of allocated capital loading applies a return rate to the capital the risk consumes after diversification; it alone is consistent with balance sheet management, and internal models have converged on it. Expense loadings, for their part, cover spending rather than risk, and are not to be confused with the risk loading.