Discrete Time Growth Optimal Investment With Costs
Posted: 28 Apr 2020
Date Written: July 16, 2002
In this work we ask how should an investor distribute wealth over various assets to maximize the growth rate of the cumulative wealth in a discrete time market with proportional transaction costs. We show that this sequential decision problem has a stationary optimal policy. In addition, we show that for all ε > 0 there exists a policy that guarantees a growth rate at most ε below optimal on almost every sample path. We also show the existence of an ε-optimal control- limit policies – control-limit policies correct the portfolio only it leaves a compact connected no-trade set. For the special case of two-asset markets, we establish that for all ε > 0 there exists a control-limit policy that is ε-optimal with probability 1.
Keywords: Growth optimal investment, transaction costs, Markov decision processes
JEL Classification: G11
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