Portfolio Selection in Stochastic Environments

In this article, I explicitly solve dynamic portfolio choice problems, up to the solution of an ordinary differential equation (ODE), when the asset returns are quadratic and the agent has a constant relative risk aversion (CRRA) coefficient. My solution includes as special cases many existing expli...

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Bibliographic Details
Published in:The Review of financial studies 2007-01, Vol.20 (1), p.1-39
Main Author: Liu, Jun
Format: Article
Language:English
Subjects:
Bond portfolios
Financial portfolios
Hedging
Interest rate risk
Interest rates
Investment risk
Investments
Mathematical models
Matrices
Optimization
Ordinary differential equations
Ornstein Uhlenbeck process
Partial differential equations
Portfolio management
Problem solving
Rates of return
Risk aversion
Risk premiums
Securities markets
Securities prices
Stochastic models
Studies
Utility functions
Volatility
Zero coupon bonds
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Summary:In this article, I explicitly solve dynamic portfolio choice problems, up to the solution of an ordinary differential equation (ODE), when the asset returns are quadratic and the agent has a constant relative risk aversion (CRRA) coefficient. My solution includes as special cases many existing explicit solutions of dynamic portfolio choice problems. I also present three applications that are not in the literature. Application 1 is the bond portfolio selection problem when bond returns are described by "quadratic term structure models." Application 2 is the stock portfolio selection problem when stock return volatility is stochastic as in Heston model. Application 3 is a bond and stock portfolio selection problem when the interest rate is stochastic and stock returns display stochastic volatility.
ISSN:0893-9454
1465-7368
DOI:10.1093/rfs/hhl001