Discrete time growth optimal investment with costs∗
نویسنده
چکیده
In this work we ask how should an investor distribute wealth over various assets to maximizethe growth rate of the cumulative wealth in a discrete time market with proportional transactioncosts. We show that this sequential decision problem has a stationary optimal policy. Inaddition, we show that for all 2 > 0 there exists a policy that guarantees a growth rate at most 2below optimal on almost every sample path. We also show the existence of an 2-optimal control-limit policies – control-limit policies correct the portfolio only it leaves a compact connectedno-trade set. For the special case of two-asset markets, we establish that for all 2 > 0 thereexists a control-limit policy that is 2-optimal with probability 1.
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