Long-Term Optimal Investment with a Generalized Drawdown Constraint

The long-term risk-sensitive optimal investment problem is studied with a generalized, nonlinear drawdown constraint. The optimal solution is constructed, using the solution to the baseline optimization problem without drawdown constraint. For the analysis, it is helpful to utilize the properties of the Azema--Yor processes associated with self-financing wealth processes. As a variant, long-term risk-sensitive optimal investment with both drawdown and floor constraints is also considered.

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