ABSTRACT: Deciding which stocks to purchase and how to optimally allocate the total investment among them is a nontrivial task for every
investor. In this article, we propose two adaptive techniques that would provide an optimal allocation maximizing the return
over the investment period. The first approach is the adaptive power method (PM) which is a modification of the proper orthogonal
decomposition method. The adaptive PM uses only the currently available information to compute the optimal allocations, yet
its long-term solution approaches the dominant eigen solution, even though that solution would require having a priori knowledge
of all stocks’ performance. The second approach is derived from the well-known Least Mean Square (LMS) method, where the optimal
allocation can be computed by adaptively steering the overall return toward a desired value. The experimental results have
indicated promising gains even when the general market trend is downward.
KeywordsAdaptive portfolio optimization-Optimal allocation-Proper orthogonal decomposition
Mathematics Subject Classification (2000)46N10-46N40
JEL Classification (2000)C44-C61
Rivista di Matematica per le Scienze Economiche e Sociali 04/2012; 33(2):81-95.