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An Extension of Some Results Due to Cox and Leland

DOI: 10.4236/jmf.2013.34043, PP. 416-425

Keywords: Path Independence, Dynamic Asset Allocation, Dynamic Optimization, Calculus of Variations

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Abstract:

We investigate an optimal portfolio allocation problem between a risky and a risk-free asset, as in [1]. They obtained explicit conditions for path-independence and optimality of allocation strategies when the price of the risky asset follows a geometric Brownian motion with constant asset characteristics. This paper analyzes and extends their results for dynamic investment strategies by allowing for non-constant returns and volatility. We adopt a continuous-time approach and appeal to well established results in stochastic calculus for doing so.

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