## Abstract

This paper analyzes the consumption investment problem of a risk averse investor in continuous time when there are several

asset classes. The classic paper in this area is due to Merton who solved the problem when the returns were assumed to be

stationary. We assume that there is time variation in the expected returns on the different assets and that this time variation arises

from movements in the underlying state variables. We formulate the investor's decision as a problem in optimal stochastic

control. Our work extends the paper by Brennan et al. (1997) to incorporate a different interest rate process. In addition

we investigate the impact of transaction costs on the stock. We employ a viscosity solution approach to the problem and to

guarantee a solution we need to impose strong assumptions.

asset classes. The classic paper in this area is due to Merton who solved the problem when the returns were assumed to be

stationary. We assume that there is time variation in the expected returns on the different assets and that this time variation arises

from movements in the underlying state variables. We formulate the investor's decision as a problem in optimal stochastic

control. Our work extends the paper by Brennan et al. (1997) to incorporate a different interest rate process. In addition

we investigate the impact of transaction costs on the stock. We employ a viscosity solution approach to the problem and to

guarantee a solution we need to impose strong assumptions.

Original language | English |
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Pages (from-to) | 201-218 |

Journal | Insurance: Mathematics and Economics |

Volume | 21 |

Publication status | Published - 1997 |

Externally published | Yes |