Catastrophe, Compounding & Consistency in Choice

TL;DR

This paper explores how different formalizations of CVaR influence decision-making, especially in long-term and psychiatric contexts, by providing examples and linking to temporal discounting.

Contribution

It introduces examples that distinguish three forms of CVaR risk compounding and links two of these forms to temporal discounting, aiding future research in risk attitudes.

Findings

Identified three structural forms of CVaR risk compounding.

Provided examples highlighting unique characteristics of each form.

Linked two CVaR approaches to temporal discounting in decision-making.

Abstract

Conditional value-at-risk (CVaR) precisely characterizes the influence that rare, catastrophic events can exert over decisions. Such characterizations are important for both normal decision-making and for psychiatric conditions such as anxiety disorders -- especially for sequences of decisions that might ultimately lead to disaster. CVaR, like other well-founded risk measures, compounds in complex ways over such sequences -- and we recently formalized three structurally different forms in which risk either averages out or multiplies. Unfortunately, existing cognitive tasks fail to discriminate these approaches well; here, we provide examples that highlight their unique characteristics, and make formal links to temporal discounting for the two of the approaches that are time consistent. These examples can ground future experiments with the broader aim of characterizing risk attitudes, especially for longer horizon problems and in psychopathological populations.