Optimal credit portfolio and consumption with regime switching and default contagion

Fei Sun, Wenyuan Wang and Kaixin Yan

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Abstract: We study an optimal portfolio and consumption problem in a regime-switching multi-name credit market with default contagion. Default events not only generate direct portfolio losses but also alter the default intensities of surviving securities. Under a Cobb-Douglas utility, the homogeneity property reduces the associated Hamilton-Jacobi-Bellman (HJB) equation to a recursive system of ordinary differential equations indexed by the default states. Solving this system backward from the all-default state, we establish existence and uniqueness of a positive classical solution, characterize the optimal feedback controls, and provide a verification theorem. Finally, numerical experiments present sensitivity analyses and comparisons across contagion settings, regimes, utilities, as well as before and after default.

Date: 2026-07, Revised 2026-09
New Economics Papers: this item is included in nep-upt
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