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Investing with liquid and illiquid assets. (English) Zbl 1403.91306

Summary: We find optimal trading policies for long-term investors with constant relative risk aversion and constant investment opportunities, which include one safe asset, liquid risky assets, and an illiquid risky asset trading with proportional costs. Access to liquid assets creates a diversification motive, which reduces illiquid trading, and a hedging motive, which both reduces illiquid trading and increases liquid trading. A further tempering effect depresses the liquid asset’s weight when the illiquid asset’s weight is close to ideal, to keep it near that level by reducing its volatility. Multiple liquid assets lead to portfolio separation in four funds: the safe asset, the myopic portfolio, the illiquid asset, and its hedging portfolio.

MSC:

91G10 Portfolio theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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