Utilities bounded below
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
It is common to work with utilities which are not bounded below, but it seems hard to reconcile this with common sense; is the plight of a man who receives only one crumb of bread a day to eat really very much worse than the plight of a man who receives two? In this paper we study utilities which are bounded below, which necessitates novel modelling elements to prevent the question becoming trivial. What we propose is that an agent is subjected to random reviews of his finances. If he is reviewed and found to be bankrupt, then he is thrown into jail, and receives some large but finite negative value. In such a framework, we find optimal investment and consumption behaviour very different from the standard story. As the agent’s wealth goes negative, he gradually abandons hope of ever becoming honest again, and plunders as much as he can before being caught. Agents with very high wealth act like standard Merton investors.
- Benartzi, S, Thaler, R (1995) Myopic loss aversion and the equity premium puzzle. Quart J Econ 10: pp. 73-92
- Carassus, L., Rasonyi, M.: On optimal investment for a behavioural investor in multiperiod incomplete market models. Preprint—arXiv:1107.1617 (2012).
- Gomes, FJ (2005) Portfolio choice and trading volume with loss-averse investors. J Bus 78: pp. 675-706 CrossRef
- Jin, H, Zhou, XY (2008) Behavioural portfolio selection in continuous time. Math Finance 18: pp. 385-426 CrossRef
- Kahneman, D, Tversky, A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47: pp. 263-291 CrossRef
- Kahneman, D, Tversky, A (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5: pp. 297-323 CrossRef
- Karatzas, I, Lehoczky, JP, Sethi, SP, Shreve, SE (1986) Explicit solution of a general consumption/investment problem. Math Oper Res 11: pp. 261-294 CrossRef
- Levy, H, Levy, M (2004) Prospect theory and mean-variance analysis. Rev Financ Stud 17: pp. 1015-1041 CrossRef
- von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton: Princeton University Press (1944)
- Rasonyi, M., Rodrigues, A.: Optimal portfolio choice for a behavioural investor in continuous-time markets. Preprint—arXiv:1202.0628 (2012).
- Reichlin, C.: Non-concave utility maximization with a given pricing measure. NCCR FINRISK—Working Paper 517 (2011).
- Ross, S.A.: Neoclassical Finance. Princeton: Princeton University Press (2005)
- Shefrin, H, Statman, M (2000) Behavioral portfolio theory. J Finance Quant Anal 35: pp. 127-151 CrossRef
- Utilities bounded below
Annals of Finance
Volume 9, Issue 2 , pp 271-289
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Expected utility
- Non-concave utility
- Von Neumann-Morgenstern preferences
- Industry Sectors