Who would invest only in the risk-free asset?

TL;DR

This paper characterizes when an investor with multiple priors and a minimax expected utility approach would choose only the risk-free asset, linking it to the existence of certain supermartingale or martingale measures.

Contribution

It provides a novel characterization of risk-only investment behavior in continuous-time markets under multiple priors and minimax utility.

Findings

Risk-only investment occurs if a prior makes all wealth processes supermartingales.

In finite or complete markets, this is equivalent to the existence of an equivalent martingale measure.

Generalizes a no betting result by Dow and Werlang.

Abstract

Within the setup of continuous-time semimartingale financial markets, we show that a multiprior Gilboa-Schmeidler minimax expected utility maximizer forms a portfolio consisting only of the riskless asset if and only if among the investor's priors there exists a probability measure under which all admissible wealth processes are supermartingales. Furthermore, we show that under a certain attainability condition (which is always valid in finite or complete markets) this is also equivalent to the existence of an equivalent (local) martingale measure among the investor's priors. As an example, we generalize a no betting result due to Dow and Werlang.