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A premium equal to expected losses would leave an insurer insolvent half the time. The standard-deviation principle adds a risk load of k·σ to compensate for volatility, and expenses are then grossed up as a share of premium.
Standard deviation principle
Premium = (E[L] + k·σ) / (1 - expense ratio)
From the return required on the capital the volatility ties up, so more volatile lines carry a higher k.
Because expenses are quoted as a percentage of premium, not of losses, so grossing up is the consistent treatment.