Small-Cost Asymptotics for Long-Term Growth Rates in Incomplete Markets

44 Pages Posted: 10 Nov 2014 Last revised: 12 Jun 2016

See all articles by Yaroslav Melnyk

Yaroslav Melnyk

affiliation not provided to SSRN

Frank Thomas Seifried

University of Trier

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

Melnyk, Yaroslav and Seifried, Frank Thomas, Small-Cost Asymptotics for Long-Term Growth Rates in Incomplete Markets (February 27, 2016). Available at SSRN: https://ssrn.com/abstract=2521036 or http://dx.doi.org/10.2139/ssrn.2521036

Yaroslav Melnyk (Contact Author)

affiliation not provided to SSRN

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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