Small‐cost asymptotics for long‐term growth rates in incomplete markets
严格分析了比例和Morton-Pliska交易成本下长期增长率的渐近行为，构建了最优策略，并发现最优Morton-Pliska策略的表现与成本增加一定倍数后的最优策略相同。
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 . 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.