Symmetrical Monotone Risk Aversion and Positive Bid-Ask Spreads
A usual argument in finance refers to no arbitrage opportunities for the positivity of the bid-ask spread. Here we follow the decision theory approach and show that if positivity of the bid-ask spread becomes identified with strong risk aversion for an expected utility market-maker, this is no longer true for a rank-dependent expected utility one. For such a decision-maker only a very weak form of risk aversion is required, a result which seems more in accordance with his actual behavior. We conclude by showing that the no-trade interval result of Dow and Werlang (1992) remains valid for a rank-dependent expected utility market-maker merely exhibiting this weak form of risk aversion.
KeywordsRisk Aversion Risky Asset Reservation Price Arbitrage Opportunity Concave Utility Function
Unable to display preview. Download preview PDF.
- Abouda, M. and Chateauneuf, A. (1998a). Positivity of bid-ask spreads and symmetrical monotone risk averse. Working Paper.Google Scholar
- Abouda, M. and Chateauneuf, A. (1998b). A characterization of the symmetrical monotone risk aversion in the RDEU model. Working Paper.Google Scholar
- Arrow, K.J. (1965). The theory of Risk aversion, Chapter 2 of Aspects of the Theory of Risk Bearing. Helsinki: Yrjo Jahnson in Saatio.Google Scholar
- Chateauneuf, A., M. D. Cohen, and I. Meilijson (1997a). New tools to better model behavior under risk and uncertainty: An overview. Finance, 18, 25–46.Google Scholar
- Chateauneuf, A., M. D. Cohen, and I. Meilijson (1997b). More pessimism than greediness: A characterization of monotone risk aversion in the RDEU model. Cahiers d’Ecomath, 97. 53.Google Scholar
- Dow, J., and Werlang S. (1992). Uncertainty aversion, risk aversion, and the optimal choice of portfolio. Econometrica, 60,No. 1, 197–204.Google Scholar
- Eeckhoudt, L. and Gollier, C. (1992). Les risques financiers, Ediscience International.Google Scholar
- Eeckhoudt, L. and Roger, P. (1998). Risk Aversion and the Bid-Ask spread. European Financial Management, Forthcoming.Google Scholar
- Roger, P. (1998). Properties of Bid-Ask spread in RDEU model. Working Paper. Université de Strasbourg. Google Scholar
- Schmeidler, D. (1989). Subjective probability and expected utility without additivity. Econometrica, 57, 517–587. First version: Subjective expected utility without additivity, Foerder Institute Working Paper (1982).Google Scholar