DONG, Yuchao; LIANG, Jin; BRAUNER, Claude-Michel

doi:10.1016/j.jde.2023.06.050

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DONG, Yuchao
School of Mathematical Sciences, Tongji University

LIANG, Jin
School of Mathematical Sciences, Tongji University

BRAUNER, Claude-Michel
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Differential Equations. 2023-11-05, vol. 372, p. 505-535

Elsevier

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In this work, a pricing model for a defaultable corporate bond with credit rating migration risk is established. The model turns out to be a free boundary problem with two free boundaries. The latter are the level sets of the solution but of different kinds. One is from the discontinuous second order term, the other from the obstacle. Existence, uniqueness, and regularity of the solution are obtained. We also prove that two free boundaries are $C^\infty$. The asymptotic behavior of the solution is also considered: we show that it converges to a traveling wave solution when time goes to infinity. Moreover, numerical results are presented.< Réduire

Mots clés en anglais

Traveling wave Free boundary problem PDE with discontinuous leading order coefficient Asymptotic behavior Credit rating migration risk model

Traveling wave

Free boundary problem

PDE with discontinuous leading order coefficient

Asymptotic behavior

Credit rating migration risk model

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Double free boundary problem for defaultable corporate bond with credit rating migration risks and their asymptotic behaviors

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