TITLE:
An Extension of Some Results Due to Cox and Leland
AUTHORS:
Andrew P. Leung, Wen Shi
KEYWORDS:
Path Independence; Dynamic Asset Allocation; Dynamic Optimization; Calculus of Variations
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.3 No.4,
October
17,
2013
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.