Time consistent portfolio strategies for a general utility function

Battle Count: 71

Highly relevant to portfolio management and asset allocation strategies. The paper provides a rigorous framework for time-consistent investment-consumption policies under general utility, which is directly applicable to institutional portfolio management, retirement planning, and behavioral finance modeling. However, it is purely theoretical with no empirical validation or backtesting, and the complete market assumption limits direct applicability to real trading environments. The feedback-form strategies (consumption-to-wealth and investment-to-wealth ratios) are practically useful for dynamic asset allocation.

High complexity. Implementation requires: (1) solving a fixed point problem for the utility-weighted discount rate via successive approximations, (2) solving a linear parabolic PDE via Feynman-Kac representation, (3) computing the x-inverse of the marginal value function, (4) performing Monte Carlo simulations for the discount rate computation, (5) solving the wealth SDE with feedback controls. The mathematical machinery (extended HJB, PDE theory, stochastic calculus) is sophisticated, and numerical stability of the fixed point iteration needs careful handling.

The paper provides complete mathematical proofs and a clear algorithm (Section 3) for constructing subgame perfect strategies. However, it is purely theoretical with no numerical examples, code, or computational experiments. Reproduction requires implementing the fixed point iteration, solving parabolic PDEs via Feynman-Kac, and performing Monte Carlo simulations for the utility-weighted discount rate. The asymptotic assumptions on the utility function (bounded relative risk aversion, Inada conditions) are clearly stated.