For a two-state unobservable stock drift, the VaR-constrained S-shaped utility problem admits a unique optimum above a critical wealth level, a limiting solution at that level, and no solution below it.
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S-shaped Utility Maximization with VaR Constraint and Partial Information
For a two-state unobservable stock drift, the VaR-constrained S-shaped utility problem admits a unique optimum above a critical wealth level, a limiting solution at that level, and no solution below it.