Nonconcave Portfolio Choice under Smooth Ambiguity

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Highly relevant for quantitative portfolio management, particularly for fund managers with option-based compensation (hedge funds, mutual funds with performance fees). The framework provides explicit trading rules that account for both ambiguity about expected returns and nonlinear payoff structures. The finding that ambiguity aversion acts as an endogenous risk constraint in convex compensation environments has direct implications for risk management policies. The all-or-nothing structure of optimal terminal wealth and the pessimistic belief distortion are practically relevant for position sizing and risk limit setting. However, the single-asset assumption and lack of transaction costs limit direct implementation in multi-asset trading systems.

The theoretical framework is highly sophisticated, combining robust representation of quasiconcave functionals, nonlinear filtering theory, martingale methods, and concavification. The five-step solution procedure requires solving nested optimization problems. The outer minimization over priors generally lacks closed-form solutions and requires numerical optimization. The filtering step involves computing conditional expectations of the drift given observed prices. The concavification step requires identifying the concave envelope of the non-concave objective. Implementation in Mathematica is feasible for the two-point prior case, but generalization to continuous prior spaces and multi-asset settings would be substantially more complex.

The paper provides detailed mathematical derivations, explicit formulas for optimal strategies (Theorem 5.1), and parameter tables for numerical experiments. Computations are performed using Mathematica 13.3, and the code is stated to be available upon request. However, no public repository is linked. The theoretical framework is fully specified with all assumptions stated, enabling replication of analytical results. Numerical experiments include specific parameter values (Table 1) and factorial designs (Table C.2).