Mathematical Finance Seminar
April 5, 2001 , 5:30 PM to 7:00 PM
Jerome Detemple, Boston University School of Management
A Monte Carlo Method for Optimal Portfolios
This paper provides (i) simulation-based approaches for the computation of
asset allocation rules, (ii) economic insights on the behavior of the
hedging components and (iii) a comparison of numerical methods. For general
utility functions with wealth-dependent risk aversion and diffusion state
variable processes, hedging demands are abtained as conditional expectations
of random variables depending on the parameters of the model, which can then
be estimated using standard simulation methods. We propose a modified
simulation approach which relies on a simple transformation of the
underlying state variables and improves the performance of Monte-Carlo
estimators of portfolio rules. Our approach is flexible and applies to (i)
arbitrary utility functions, (ii) any finite number of state variables,
(iii) general diffusion processes for state variables and (iv) any finite
number of assets. The procedure is implemented for a class of multivariate
nonlinear diffusions for the market price of risk (MPR), the interest rate
(IR) and other factors (dividends). After calibrating the models to the data
we document the portfolio behavior. We find that intertemporal hedging
demands (i) significantly increase the demand for stocks and (ii) exhibit
low volatility. In addition we show that (iii) non-linearities are
important: significant biases in allocation rules are documented if one uses
typical (linear-affine) processes calibrated to the data.