Small-Cost Asymptotics for Long-Term Growth Rates in Incomplete Markets
44 Pages Posted: 10 Nov 2014 Last revised: 12 Jun 2016
Date Written: February 27, 2016
Abstract
This article provides a rigorous asymptotic analysis of long-term growth rates under both proportional and Morton-Pliska transaction costs. We consider a general incomplete financial market with an unspanned Markov factor process that includes the Heston stochastic volatility model and the Kim-Omberg stochastic excess return model as special cases. Using a dynamic programming approach, we determine the leading-order expansions of long-term growth rates and explicitly construct strategies that are optimal at the leading order. We further analyze the asymptotic performance of Morton-Pliska strategies in settings with proportional transaction costs. We find that the performance of the optimal Morton-Pliska strategy is the same as that of the optimal one with costs increased by a factor of √2. Finally, we demonstrate that our strategies are in fact pathwise optimal, in the sense that they maximize the long-run growth rate path by path. All our results are substantiated by verification arguments.
Keywords: transaction costs, Morton-Pliska, leading-order optimality, asymptotic expansion, Kelly criterion, pathwise optimality
JEL Classification: G11, C61
Suggested Citation: Suggested Citation