Convergence Rates of Turnpike Theorems for Portfolio Choice in Stochastic Factor Models

Battle Count: 79

The paper provides important theoretical foundations for long-term portfolio management. The turnpike theorem implies that for very long investment horizons, optimal strategies converge to CRRA (constant relative risk aversion) strategies regardless of the specific utility function. The convergence rates inform practitioners about how quickly this approximation becomes valid. The decomposition into myopic and hedging components is directly relevant to multi-asset portfolio construction. The collective investment application is relevant for fund management. However, the results are primarily theoretical and do not provide directly implementable trading algorithms.

The paper requires advanced mathematical knowledge including Malliavin calculus, stochastic differential equations, martingale theory, Girsanov's theorem, matrix Riccati equations, and viscosity solutions. The theoretical framework involves multiple layers of assumptions and complex probabilistic arguments. Implementing the theoretical results would require solving systems of ODEs (Riccati equations) and computing expectations under multiple probability measures. The paper does not provide any code or numerical algorithms.

The paper is entirely theoretical with complete mathematical proofs provided in Section 3 and Appendices A-D. All assumptions are clearly stated (Assumptions 2.1-2.5), and theorems are rigorously proved. However, there are no numerical examples, simulations, or code to reproduce. The mathematical framework is self-contained with detailed derivations of Malliavin calculus results, option pricing theory, and Riccati equation properties.