Portfolio Optimization Models on Infinite-Time Horizon

T. Pang
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T. Pang: North Carolina State University

Journal of Optimization Theory and Applications, 2004, vol. 122, issue 3, No 7, 573-597

Abstract: Abstract A portfolio optimization problem on an infinite-time horizon is considered. Risky asset prices obey a logarithmic Brownian motion and interest rates vary according to an ergodic Markov diffusion process. The goal is to choose optimal investment and consumption policies to maximize the infinite-horizon expected discounted hyperbolic absolute risk aversion (HARA) utility of consumption. The problem is then reduced to a one-dimensional stochastic control problem by virtue of the Girsanov transformation. A dynamic programming principle is used to derive the dynamic programming equation (DPE). The subsolution/supersolution method is used to obtain existence of solutions of the DPE. The solutions are then used to derive the optimal investment and consumption policies. In addition, for a special case, we obtain the results using the viscosity solution method.

Keywords: Portfolio optimization; dynamic programming equations; subsolutions and supersolutions (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (8)

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DOI: 10.1023/B:JOTA.0000042596.26927.2d

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