• Corpus ID: 50189282

Lifetime Portfolio Selection under Uncertainty: the Continuous-time Case

@inproceedings{Dreyfus2006LifetimePS,
  title={Lifetime Portfolio Selection under Uncertainty: the Continuous-time Case},
  author={Stuart E. Dreyfus},
  year={2006}
}

• S. Dreyfus
• Published 2006
• Economics

M OST models of portfolio selection have been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model where his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic. P . A. Samuelson has developed a similar model in discrete-time for more general probability distributions in a companion paper C81. I derive the optimality equations for a multiasset problem when the rate of returns are generated by a Wiener Brownian-motion process. A particular case examined in detail is the two-asset model with constant relative riskaversion or iso-elastic marginal utility. An explicit solution is also found for the case of constant absolute risk-aversion. The general technique employed can be used to examine a wide class of intertemporal economic problems under uncertainty. In addition to the Samuelson paper [S], there is the multi-period analysis of Tobin [9]. Phelps [6] has a model used to determine the optimal consumption rule for a multi-period example where income is partly generated by an asset with an uncertain return. Mirrless [ S ] has developed a continuous-time optimal consumption model of the neoclassical type with technical progress a random variable.