Risk Apportionment: The Dual Story

TL;DR

This paper develops a dual framework for risk apportionment using model-free preferences, providing new insights into dual concepts like prudence and temperance, and linking the derivatives of probability weighting to portfolio choices.

Contribution

It introduces a dual perspective to risk apportionment, characterizes dual concepts, and connects derivatives of probability weighting to portfolio optimization and self-protection.

Findings

Dual preferences offer an intuitive interpretation of risk concepts.

Sign of the third derivative relates to self-protection strategies.

Results inform optimal portfolio choice based on probability weighting derivatives.

Abstract

By specifying model free preferences towards simple nested classes of lottery pairs, we develop the dual story to stand on equal footing with that of (primal) risk apportionment. The dual story provides an intuitive interpretation, and full characterization, of dual counterparts of such concepts as prudence and temperance. The direction of preference between these nested classes of lottery pairs is equivalent to signing the successive derivatives of the probability weighting function within Yaari's (1987) dual theory. We explore implications of our results for optimal portfolio choice and show that the sign of the third derivative of the probability weighting function may be naturally linked to a self-protection problem.