Optimal investment under high-water mark contracts with model ambiguity

This paper incorporates the ambiguities of the risky asset and the exogenous shock to explore how the two ambiguities influence the hedge funds model. We find the ambiguity of the risky asset makes the manager more risk averse and invest less. While the ambiguity of the exogenous shock induce the manager adopt radical investment way and invest more. But at the lower and upper bounds, both ambiguities do not work any more. The manager's total value is eroded by either of the two ambiguities. Although the manager adopts different investment strategies for the two ambiguities, her income makes little difference. In high uncertain context of the external shock or the risky asset, manager's rigorous investment strategies can protect the values of the investors and the entire fund. Both of the ambiguities have negative influences on the incentive fee and also reduce the proportion of incentive fee in her total income.