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[{"key": "dc.contributor.advisor", "value": "Geiss, Christel", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Kohal, Johannes", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2019-02-18T09:40:15Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2019-02-18T09:40:15Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2018", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/62821", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 opinn\u00e4ytety\u00f6ss\u00e4 k\u00e4sitell\u00e4\u00e4n taivutettuihin L\u00e9vy-prosesseihin liittyvi\u00e4 poistumisongelmia. Poistumisongelmilla tarkoitetaan arvojoukkov\u00e4lin [a,c] p\u00e4\u00e4tepisteiden ylityksiin liittyvi\u00e4 ongelmia. Taivutettu L\u00e9vy-prosessi (englanniksi refracted L\u00e9vy process) m\u00e4\u00e4ritell\u00e4\u00e4n ty\u00f6ss\u00e4 siten, ett\u00e4 se on prosessi, jota taivutetaan alasp\u00e4in lineaarisen suoran avulla prosessin ollessa annetun arvon b yl\u00e4puolella, miss\u00e4 b kuuluu v\u00e4lille [a,c]. Matemaattisesti taivutettu L\u00e9vy-prosessi m\u00e4\u00e4ritell\u00e4\u00e4n stokastisen differentiaaliyht\u00e4l\u00f6n ja spektraalisti negatiivisen L\u00e9vy-prosessin avulla. Spektraalisti negatiivinen L\u00e9vy-prosessi (englanniksi spectrally negative L\u00e9vy process) on L\u00e9vy-prosessi, jolla on vain negatiivisia hyppyj\u00e4. Spektraalisti negatiivisilla L\u00e9vy-prosesseilla voidaan muun muassa mallintaa vakuutusyhti\u00f6iden p\u00e4\u00e4omaa. Ty\u00f6ss\u00e4 taivutetun L\u00e9vy-prosessin U poistumisongelmien yht\u00e4l\u00f6t johdetaan prosessiin U liittyvien spektraalisti negatiivisten L\u00e9vy-prosessien poistumisongelmien avulla. Spektraalisti negatiivisiin L\u00e9vy-prosesseihin liittyvien poistumisongelmien yht\u00e4l\u00f6iss\u00e4 k\u00e4ytet\u00e4\u00e4n skaalafunktioita (englanniksi scale function). Skaalafunktiot m\u00e4\u00e4ritell\u00e4\u00e4n Laplace-muunnoksen avulla ja ne ovat yksik\u00e4sitteisi\u00e4 annetun spektraalisti negatiivisen L\u00e9vy-prosessin suhteen. \nTy\u00f6n lopussa esitell\u00e4\u00e4n riskimalli, jossa taivutettu L\u00e9vy-prosessi U mallintaa yrityksen taloudellista tilannetta. Poistumisongelmien avulla johdetaan yht\u00e4l\u00f6t, joiden avulla voidaan laskea prosessin U mallintaman yrityksen konkurssin todenn\u00e4k\u00f6isyys. \nTy\u00f6 pohjautuu Jean-Francois Renaud'n ty\u00f6h\u00f6n On the time spent in the red by a refracted L\u00e9vy risk process \n(J. Appl. Prob. 51, 1171-1188 (2014)).", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2019-02-18T09:40:15Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2019-02-18T09:40:15Z (GMT). No. of bitstreams: 0\n Previous issue date: 2018", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "54", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "scale functions", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "spectrally negative L\u00e9vy process", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "exit problems", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "refracted L\u00e9vy process", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "probability of bankruptcy", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Scale function approach to exit problems of refracted L\u00e9vy risk processes", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201902181526", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Stokastiikka ja todenn\u00e4k\u00f6isyysteoria", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Stochastics and Probability", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "todenn\u00e4k\u00f6isyyslaskenta", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "probability calculation", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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