Betting Around the Clock: Time Change and Long Term Model Risk

Battle Count: 110

Highly relevant for long-term portfolio management and Kelly criterion applications. The paper demonstrates that the standard Kelly rule is suboptimal (too aggressive) when returns follow non-lognormal distributions common in practice (e.g., Variance Gamma). This has direct implications for position sizing in quantitative strategies. However, the paper is primarily theoretical and does not provide a complete trading system or backtesting framework. The model risk discussion is crucial for practitioners using growth-optimal portfolio approaches.

The core analytical results (generalized compounding formula, ruin thresholds) are mathematically sophisticated, requiring knowledge of semi-martingale theory, moment generating functions, and time change processes. However, the numerical implementation for specific models (VG, IG) involves straightforward computation of MGFs and their inverses. The acceptability index framework adds complexity through distorted probability measures and Choquet integrals. Practical implementation requires estimating the stochastic clock variance, which introduces additional complexity.

The paper is primarily analytical with closed-form results for specific models (VG, IG). Numerical examples are based on the Rotando-Thorp (1992) framework with specified parameters. Parameter estimates for the VG model are taken from published literature (Hurst et al. 1997, Madan-Carr-Chang 1998, Seneta 2004). No code or raw data is provided, but the mathematical derivations are self-contained and reproducible.