Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary
In this paper, we study the nonlinear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation of this equation, which is also related to the supercooled Stefan problem, as a structural cred...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Cambridge University Press
2019
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| _version_ | 1797105005662044160 |
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| author | Lipton, A Kaushansky, V Reisinger, C |
| author_facet | Lipton, A Kaushansky, V Reisinger, C |
| author_sort | Lipton, A |
| collection | OXFORD |
| description | In this paper, we study the nonlinear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation of this equation, which is also related to the supercooled Stefan problem, as a structural credit risk model with default contagion in a large interconnected banking system. Using the method of heat potentials, we derive a coupled system of Volterra integral equations for the transition density and for the loss through absorption. An approximation by expansion is given for a small interaction parameter. We also present a numerical solution algorithm and conduct computational tests. |
| first_indexed | 2024-03-07T06:41:22Z |
| format | Journal article |
| id | oxford-uuid:f965487a-5de3-4117-9c59-d6fe7ec183f1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:41:22Z |
| publishDate | 2019 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:f965487a-5de3-4117-9c59-d6fe7ec183f12022-03-27T12:57:37ZSemi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundaryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f965487a-5de3-4117-9c59-d6fe7ec183f1EnglishSymplectic Elements at OxfordCambridge University Press2019Lipton, AKaushansky, VReisinger, CIn this paper, we study the nonlinear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation of this equation, which is also related to the supercooled Stefan problem, as a structural credit risk model with default contagion in a large interconnected banking system. Using the method of heat potentials, we derive a coupled system of Volterra integral equations for the transition density and for the loss through absorption. An approximation by expansion is given for a small interaction parameter. We also present a numerical solution algorithm and conduct computational tests. |
| spellingShingle | Lipton, A Kaushansky, V Reisinger, C Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary |
| title | Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary |
| title_full | Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary |
| title_fullStr | Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary |
| title_full_unstemmed | Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary |
| title_short | Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary |
| title_sort | semi analytical solution of a mckean vlasov equation with feedback through hitting a boundary |
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