This paper studies a portfolio insurance problem with liquidity risk. We consider an investor who wants to maximize the expected growth rate of wealth in a low liquid market. The investor can trade assets only at random times and his wealth must not fall below a predetermined floor. We find the optimal expected growth rate and an optimal strategy. The optimal strategy is closely related with a traditional constant proportion portfolio insurance strategy. Also we show that the same strategy maximizes the growth rate almost surely. Further we study the floor effect on the growth rate.
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