The purpose of this editorial is to consider the existence and implications of epistemological constraints in the field of risk finance arising from statistical inequalities similar to the Cramér‐Rao lower bound (CRLB) of statistical estimation theory and the Heisenberg uncertainty principle (HUP) of quantum physics.
The conceptual equivalence of the CRLB to the HUP suggests that certain statistical inequalities in the field of risk finance might imply practical constraints on knowledge analogous to those encountered in the measurement of subatomic particles. To explore this possibility, the editorial first considers the tradeoff between the variability of an estimator and the variability of the score of the associated joint probability distribution, and then interpret the latter quantity in a manner permitting the identification of real‐world counterparts.
Under certain simple assumptions, the editorial finds that the estimation of two fundamental actuarial quantities of property‐liability insurance – the expected individual loss amount and the expected discounted total claim payments – is subject to a type of uncertainty principle in that a high degree of accuracy in measuring one quantity implies a low degree of accuracy in measuring the other, and vice versa. Since the principle holds in the limit only as one, but not both, of the two quantities is measured with certainty, the editorial characterizes it as a semi‐uncertainty principle. This principle is likely to result in certain economic behaviors by insurance companies that may be verified empirically.
The editorial provides a concrete example of two‐financial quantities whose estimation is governed by a type of uncertainty principle similar to Heisenbergs.
CitationDownload as .RIS
Emerald Group Publishing Limited
Copyright © 2010, Emerald Group Publishing Limited