Optimal Credit Portfolio and Consumption with Regime Switching and Default Contagion

Battle Count: 115

The paper provides a rigorous theoretical framework for optimal portfolio-consumption decisions in credit markets with regime switching and default contagion. While primarily a mathematical finance paper, the feedback control characterization (optimal portfolio fractions and consumption rates as functions of time, regime, and default state) has direct implications for systematic credit portfolio management. The sensitivity analyses reveal how default intensities, volatility, regime transitions, and risk preferences affect optimal allocations. However, the paper is theoretical and does not provide backtesting on real data or trading signals directly.

Implementation requires solving a recursive system of coupled nonlinear ODEs indexed by default states (2^n states for n assets). The backward induction from all-default to all-alive states, combined with the truncation argument for handling singularities at zero, adds significant complexity. The portfolio minimization at each default state involves solving a convex optimization problem. For n=2, there are 4 default states; for larger portfolios, the state space grows exponentially. The verification theorem requires careful handling of localization, maximal integrability conditions, and Doob's inequality.

The paper provides detailed benchmark parameters (Section 4.1) including market coefficients, default intensities, generator matrix, and utility parameters. The recursive ODE system is fully specified. However, no code or computational scripts are provided. The numerical experiments involve solving coupled nonlinear ODE systems which require careful implementation of the backward induction and truncation procedures. The mathematical derivations are complete and self-contained.