Optimal Credit Portfolio and Consumption with Regime Switching and Default Contagion

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The paper provides a rigorous theoretical framework for optimal credit portfolio management under regime switching and default contagion. While directly relevant to credit portfolio managers and risk managers, it is purely theoretical without numerical results or trading signals. The feedback control characterization could inform systematic credit portfolio strategies, but practical implementation would require significant additional work including calibration, numerical solution of the recursive system, and empirical validation.

The theoretical framework involves solving a recursive system of nonlinear ODEs indexed by 2^n default states (where n is the number of risky assets). The backward induction procedure, truncation arguments, and verification theorem are mathematically sophisticated. Numerical implementation would require solving coupled nonlinear ODE systems at each default state, with the system size growing exponentially in the number of assets. The optimal feedback controls involve solving convex minimization problems at each state.

The paper is purely theoretical with complete mathematical proofs. All equations, lemmas, and theorems are self-contained and verifiable. However, there are no numerical experiments or code to reproduce. The recursive ODE system could be solved numerically given the explicit structure, but no such implementation is provided.