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Optimal investment strategy under time-inconsistent preferences and high-water mark contract. (English) Zbl 1408.91188

Summary: This paper considers the optimal investment problem for a fund manager who has time-inconsistent preferences and is compensated with a HWM contract. The time preferences of fund manager is described by the stochastic hyperbolic discounting function. The closed-form solution under certain conditions is provided by applying the dynamic programming approach. Interestingly, we find that the sophisticated fund manager is present-biased. The more the fund manager has present-biased preference, there is the greater inclination to increase the proportion in risky asset.

MSC:

91G10 Portfolio theory
91G80 Financial applications of other theories
49L20 Dynamic programming in optimal control and differential games
93E20 Optimal stochastic control
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