Asymptotics for optimal investment with high-water mark fee
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This dissertation studies the problem of optimal investment in a fund charging high-water mark fees. We consider a market consisting of a riskless money-market account and a fund charging high-water mark fees at rate λ, with share price given exogenously as a geometric Brownian motion. A small investor invests in this market on an infinite time horizon and seeks to maximize expected utility from consumption rate. Utility is taken to be constant relative risk aversion (CRRA). In this setting, we study the asymptotic behavior of the value function for small values of the fee rate λ. In particular, we determine the first and second derivatives of the value function with respect to λ. We then exhibit for each λ explicit sub-optimal feedback investment and consumption strategies with payoffs that match the value function up to second order in λ.