Stochastic Control for Asset Management

James J. Kung¹, Wing-Keung Wong², E-Ching Wu³

¹Department of International Business, Ming Chuan University, Taipei City.
²Department of Economics, Hong Kong Baptist University, Hong Kong, China.
³Department of Finance, Providence University, Taichung.

DOI: 10.4236/jmf.2013.31005                

Abstract

An investor is often faced with the investment situation in which he/she has to decide how to allocate his/her limited funds optimally among different assets to maximize his/her expected utility over the holding period. To this end, this study sets up a dynamic model driven by three assets to characterize the stochastic nature of the securities market and uses stochastic control to derive an explicit formula for the optimal fraction invested in each of the three assets for an investor with a power utility and a holding period of 10 years. Using estimated parameter values as inputs and implicit finite difference method, we determine numerically the optimal percentages invested in the three assets at each time over the holding period for both less risk-averse and more risk-averse investors.

 

Keywords

Stochastic Control; Three-Asset Model; Vasicek Interest Rate Model; Optimal Fraction

Conflicts of Interest

The authors declare no conflicts of interest.

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