Articlebronze1999

The asymptotic elasticity of utility functions and optimal investment in incomplete markets

948 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Economic theories and models Risk and Portfolio Optimization

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.

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References

2007Brownian Motion and Stochastic Calculus 1971Optimum consumption and portfolio rules in a continuous-time model 1969Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case 1991Brownian motion and stochastic calculus 1991Continuous-Time Finance.1969Lifetime Portfolio Selection By Dynamic Stochastic Programming 1989Optimal consumption and portfolio policies when asset prices follow a diffusion process 2008A General Version of the Fundamental Theorem of Asset Pricing (1994)

Cited by

2004Arbitrage Theory in Continuous Time 2005Utility maximization in incomplete markets 2002Exponential Hedging and Entropic Penalties 2007The numéraire portfolio in semimartingale financial models 2000Efficient hedging: Cost versus shortfall risk 2002The cumulant process and Esscher's change of measure 2001Optimal investment in incomplete markets when wealth may become negative

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