OPTIMAL INVESTMENT DECISIONS FOR A PORTFOLIO WITH A ROLLING HORIZON BOND AND A DISCOUNT BOND

Tomasz R. Bielecki, Stanley Pliska and Jiongmin Yong
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Tomasz R. Bielecki: Applied Mathematics Department, Illinois Institute of Technology, Chicago IL 60616, USA
Stanley Pliska: Department of Finance, University of Illinois at Chicago, Chicago IL 60607-7124, USA
Jiongmin Yong: Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics, and Institute of Mathematical Finance, Fudan University, Shanghai 200433, China

International Journal of Theoretical and Applied Finance (IJTAF), 2005, vol. 08, issue 07, 871-913

Abstract: An optimal investment problem is considered for a continuous-time market consisting of the usual bank account, a rolling horizon bond, and a discount bond whose maturity coincides with the planning horizon. Two economic factors, namely, the short rate and the risk-free yield of some fixed maturity, are modeled as Gaussian processes. For the problem of maximizing expected CRRA utility of terminal wealth, the optimal portfolio is obtained through a Bellman equation. The results are noteworthy because the discount bond, which is the riskless asset for the investor, causes a degeneracy due to its zero volatility at the planning horizon. Indeed, this delicate matter is treated rigorously for what seems to be the first time, and it is shown that there exists an optimal, admissible (but unbounded) trading strategy.

Keywords: Rolling horizon bond; discount bond; Bellman equation; Riccati equation; stochastic interest rates; optimal portfolio (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219024905003335

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