{
  "id": "1807.05126",
  "version": "v1",
  "published": "2018-07-13T15:15:04.000Z",
  "updated": "2018-07-13T15:15:04.000Z",
  "title": "At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem",
  "authors": [
    "Sean Ledger",
    "Andreas Sojmark"
  ],
  "comment": "21 pages, 1 figure",
  "categories": [
    "math.PR",
    "math.AP",
    "q-fin.MF"
  ],
  "abstract": "We extend a model of feedback and contagion in large mean-field systems by introducing a common source of noise driven by Brownian motion. Although the dynamics in the model are continuous, the feedback effect can lead to jump discontinuities in the solutions --- i.e. 'blow-ups'. We prove existence of solutions to the corresponding conditional McKean--Vlasov equation and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-13T15:15:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H15",
      "60H30",
      "82C22"
    ],
    "keywords": [
      "conditional mckean-vlasov problem",
      "common noise",
      "corresponding conditional mckean-vlasov equation",
      "large mean-field systems",
      "prevent blow-ups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}