Continuous-Time Multivariate Strategic Asset Allocation

This paper develops a continuous-time portfolio optimization approach for making multivariate optimal asset allocation decisions. The assets are modelled as geometric Brownian motion with time-varying stochastic mean returns. The mean returns are directly affected by financial and economic factors. These factors are modelled as stochastic Gaussian processes and the mean return of the assets are an affine function of the factor levels. The portfolio optimization problem with maximizing expected power and exponential utility over terminal wealth is solved in closed-form for m factors and n assets. The factor dynamics and the asset price dynamics are correlated. The optimal unconstrained portfolio weights are affine functions of the factor levels with time-varying parameters. The methods for power utility maximization are then applied to German and UK data with two assets and four factors. The performance of the portfolio is evaluated using different levels of risk aversion and time horizons and is compared to the respective stock market indices.

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