Managing Risk Across Time: An Intertemporal Spectral Risk Measures Framework for Multi-Period Portfolio Optimization

This paper introduces a novel framework for multi-period portfolio optimization that incorporates intertemporal spectral risk measures (ISRMs). The model dynamically manages risk by considering both tail risk, through spectral risk measures, and overall portfolio volatility, through variance, across multiple time periods. This approach allows investors to specify time-varying risk preferences via a spectral function, making it particularly suitable for investors with evolving risk management needs. We develop an efficient solution methodology based on the Progressive Hedging Algorithm (PHA), enhanced with specialized reformulations to handle linkage objectives and constraints inherent in the multi-period setting. We establish the theoretical convergence properties of our algorithm, demonstrating a q-linear convergence rate under mild conditions. Numerical experiments validate the effectiveness of our approach, showing that the intertemporal weighting scheme provides more consistent risk management across the investment horizon compared to terminal-focused strategies. Notably, our approach exhibits superior downside risk protection, as evidenced by improved Sortino and Omega ratios, and generates more balanced wealth distributions with moderate tails. These findings offer valuable insights and practical tools for investors seeking to implement dynamic risk-management strategies that account for both intermediate and terminal objectives.