The relationship between two kinds of structural credit migration models

Yang Lin; Jin Liang; Yang Lin; Jin Liang

doi:10.3934/math.2024219

AIMS Mathematics

2024, Volume 9, Issue 2: 4551-4561. doi: 10.3934/math.2024219

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Research article

The relationship between two kinds of structural credit migration models

Yang Lin ^1,2,
Jin Liang ^{2
,
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1.
Postdoctoral Research Center, Industrial and Commercial Bank of China, Beijing 100140, China
2.
School of Mathematical Sciences, Tongji University, Shanghai 200092, China

Received: 02 November 2023 Revised: 30 December 2023 Accepted: 08 January 2024 Published: 18 January 2024
MSC : 35K40, 91G40

In this paper, we presented an asymptotic relationship between the single threshold model and the model with different upgrade and downgrade thresholds for credit migration problems with fixed boundaries. By partial differential equation (PDE) techniques, we proved that the solution of the asymmetric threshold problem converges to that of a single threshold problem uniformly as one of the asymmetric thresholds approaches the other.
- credit migration risk,
- different upgrade and downgrade thresholds,
- asymptotic behavior,
- structural model,
- corporate bond pricing
Citation: Yang Lin, Jin Liang. The relationship between two kinds of structural credit migration models[J]. AIMS Mathematics, 2024, 9(2): 4551-4561. doi: 10.3934/math.2024219

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Abstract

In this paper, we presented an asymptotic relationship between the single threshold model and the model with different upgrade and downgrade thresholds for credit migration problems with fixed boundaries. By partial differential equation (PDE) techniques, we proved that the solution of the asymmetric threshold problem converges to that of a single threshold problem uniformly as one of the asymmetric thresholds approaches the other.

References

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