Double free boundary problem for defaultable corporate bond with credit rating migration risks and their asymptotic behaviors
Language
en
Article de revue
This item was published in
Journal of Differential Equations. 2023-11-05, vol. 372, p. 505-535
Elsevier
English Abstract
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 ...Read more >
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.Read less <
English Keywords
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
Origin
Hal imported