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[{"key": "dc.contributor.advisor", "value": "Geiss, Stefan", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "H\u00e4nninen, Henri", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2022-08-01T05:20:31Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2022-08-01T05:20:31Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2022", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/82420", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa tarkastelemme henkivakuutuksen varantoa. Mallinnamme henkivakuutusta Markovin prosessin avulla, ja varannon m\u00e4\u00e4rittelyyn ja mallintamiseen k\u00e4yt\u00e4mme Markovin ketju BSDE:it\u00e4 (Markovin ketju takaperoinen stokastinen differentiaaliyht\u00e4l\u00f6). Seuraamme ensisijaisena l\u00e4hteen\u00e4 Boualem Djehichen ja Bj\u00f6rn L\u00f6fdahlin artikkelia Nonlinear reserving in life insurance: Aggregation and mean-field approximation. Muotoilemme ja todistamme ensimm\u00e4isten lukujen v\u00e4itteet, osittain eri oletuksin. \nMarkovin ketju BSDE:iden m\u00e4\u00e4rittely\u00e4 varten tarvitsemme sopivan yleist\u00e4 stokastisen integroinnin ja Markovin prosessien teoriaa. Annamme tarvittavat esitiedot todenn\u00e4k\u00f6isyysteoriasta ja integroinnin teoriasta. Esittelemme martingaalien teoriaa, jotta voimme m\u00e4\u00e4ritell\u00e4 stokastisen integraalin semimartingaalien suhteen.\nTodistamme olemassaolon ja yksik\u00e4sitteisyyden Markovin ketju BSDE:iden ratkaisulle. Todistus mukailee vastaavaa Brownin liikkeen tapausta. Tutkimme my\u00f6s erityistapausta, jossa Markovin ketju BSDE:iden ensimm\u00e4isen asteen termin kerroinfunktio on deterministinen Markovin ketjun ja varannon funktio. Osoitamme, ett\u00e4 t\u00e4ll\u00f6in varanto on deterministinen Markovin ketjun funktio. Todistamme, ett\u00e4 t\u00e4ss\u00e4 tapauksessa varanto toteuttaa ep\u00e4lineaarisen Thielen yht\u00e4l\u00f6n.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "In this thesis we introduce Markov chain backward stochastic differential equations (BSDE), in aim to let us model insurance policies with payments dependent on the policy reserve. We prove the existence and uniqueness of a\nsolution to the BSDEs. In the case of a deterministic driver for the BSDE, we prove that the modeled reserve is a solution to a nonlinear Thiele equation. For our main results we follow the article Nonlinear reserving in life insurance:\nAggregation and mean-field approximation by Boualem Djehiche and Bj\u00f6rn L\u00f6fdahl.\nTo define Markov chain BSDEs and prove our main results, we need suitably general theory of stochastic integration and Markov processes. After preliminary results, we define the stochastic integral with respect to semimartingales. Then we introduce Markov processes to study the model of the insurance policy.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2022-08-01T05:20:31Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2022-08-01T05:20:31Z (GMT). No. of bitstreams: 0\n Previous issue date: 2022", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "51", "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": "stochastic differential equations", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "probability theory", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "stochastic calculus", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Markov chain backward stochastic differential equations in modeling insurance policy", "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-202208013976", "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": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "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": "Markovin ketjut", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "stokastiset prosessit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "vakuutusmatematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "Markov chains", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "stochastic processes", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "mathematics", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "insurance mathematics", "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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