The asymptotic elasticity of utility functions and optimal investment in incomplete markets
Open Access
- 1 August 1999
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 9 (3) , 904-950
- https://doi.org/10.1214/aoap/1029962818
Abstract
The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less than 1.Keywords
This publication has 25 references indexed in Scilit:
- A bipolar theorem forLecture Notes in Mathematics, 1999
- A Simple Counterexample to Several Problems in the Theory of Asset PricingMathematical Finance, 1998
- Optional decomposition and Lagrange multipliersFinance and Stochastics, 1997
- Optional decompositions under constraintsProbability Theory and Related Fields, 1997
- Optional decomposition of supermartingales and hedging contingent claims in incomplete security marketsProbability Theory and Related Fields, 1996
- A Martingale Representation Result and an Application to Incomplete Financial MarketsMathematical Finance, 1992
- A variational problem arising in financial economicsJournal of Mathematical Economics, 1991
- Optimum consumption and portfolio rules in a continuous-time modelJournal of Economic Theory, 1971
- Lifetime Portfolio Selection By Dynamic Stochastic ProgrammingThe Review of Economics and Statistics, 1969
- Lifetime Portfolio Selection under Uncertainty: The Continuous-Time CaseThe Review of Economics and Statistics, 1969