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A Critique of Risk-Adjusted Discounting-Proceedings ASTIN 2001-Washington, United States of America

The adjustment of the discount function for risk has led actuaries and other financial decision-makers into a labyrinth, some of whose branches are risk-adjusted returns, capital allocation, and piecemeal risk loads. This paper will define a stochastic cash flow, and will prove that to free the pricing of such a cash flow from arbitrage one must adjust its probability measure, not the discount function. In a less theoretical vein, the paper will proceed to show from simple examples the inconsistency of risk-adjusting the discount function. Then it will draw out implications for actuarial practice, one of the most important being that there are risk elements for which premiums neither can nor should be loaded. Five appendices delve into these and related matters, and make clear that the ideas herein are mere beginnings.