Merton's Problem with Recursive Perturbed Utility

Battle Count: 141

The paper provides a theoretical framework for portfolio optimization under behavioral preferences for randomization. While not directly producing trading signals or algorithms, it offers insights into: (1) how behavioral biases affect optimal portfolio allocation, (2) the financial cost of non-standard preferences, (3) Gaussian randomized policies that could inform stochastic execution strategies, (4) the interaction between hedging demand and randomization in incomplete markets. The closed-form variance and PDE-based mean provide actionable structure for implementation.

High complexity: requires solving a nonlinear PDE (equation 15) for the mean policy, implementing Gaussian randomized controls, handling BSDE characterization, and performing asymptotic expansions. The variance has a closed form (lambda/(gamma*sigma^2)), but the mean requires numerical PDE solutions in general. The recursive utility structure adds computational complexity compared to standard Merton. However, the Gaussian structure simplifies simulation.

Purely theoretical paper with complete mathematical proofs. All results are analytical (Theorems 1-4, Propositions 1-2, Lemma 1). No numerical experiments or code required. Reproducibility depends on verifying the mathematical derivations. The PDE (15) and BSDE (33) characterizations are fully specified.