Small‐cost asymptotics for long‐term growth rates in incomplete markets

Small‐cost asymptotics for long‐term growth rates in incomplete markets This paper 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Finance Wiley

Small‐cost asymptotics for long‐term growth rates in incomplete markets

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
© 2018 Wiley Periodicals, Inc.
ISSN
0960-1627
eISSN
1467-9965
D.O.I.
10.1111/mafi.12152
Publisher site
See Article on Publisher Site

Abstract

This paper 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.

Journal

Mathematical FinanceWiley

Published: Jan 1, 2018

Keywords: ; ; ; ; ;

References

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