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[{"key": "dc.contributor.advisor", "value": "Geiss, Christel", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "L\u00e4hdem\u00e4ki, Sami", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2021-10-04T09:46:43Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2021-10-04T09:46:43Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2021", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/78002", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa perehdyt\u00e4\u00e4n odotusarvo-varianssi -suojausongelmaan (engl.\nmean-variance hedging problem) ep\u00e4t\u00e4ydellisill\u00e4 sijoitusmarkkinoilla. P\u00e4\u00e4l\u00e4hteen\u00e4 seuraamme\nX. Xuen, J. Zhanging ja C. Wengin artikkelia Mean-variance Hedging with\nBasis risk. Oletamme aikav\u00e4lin [0; T] jollekin T > 0, arbitraasivapaan sijoitusmarkkinan,\nyhden riskitt\u00f6m\u00e4n sijoituskohteen ja (m+ 1) riskillist\u00e4 sijoituskohdetta. N\u00e4iden\nkohteiden arvon oletetaan noudattavan stokastisia differentiaaliyht\u00e4l\u00f6it\u00e4, joissa kertoimet\novat deterministisi\u00e4 ja Borel-mitallisia. Yksi n\u00e4ist\u00e4 riskillisist\u00e4 sijoituskohteista\noletetaan liittyv\u00e4n vaateeseen, jolle haluamme rakentaa suojaussalkun. T\u00e4t\u00e4 kyseist\u00e4 sijoituskohdetta ei voida k\u00e4ytt\u00e4\u00e4 suojaussalkun rakentamisessa, mik\u00e4 aiheuttaa\nsijoitusmarkkinan ep\u00e4t\u00e4ydellisyyden. T\u00e4m\u00e4n vuoksi my\u00f6s t\u00e4ydellisen suojaussalkun\nrakentaminen ei ole mahdollista.\nM\u00e4\u00e4rittelemme voittoa/tappiota kuvaavan satunnaismuuttujan k\u00e4ytt\u00e4m\u00e4ll\u00e4 suojaussalkun\narvon ja vaateen erotusta. Odotusarvo-varianssi -kriteeri\u00e4 k\u00e4ytet\u00e4\u00e4n t\u00e4h\u00e4n\nsatunnaismuuttujaan ja t\u00e4m\u00e4n johdosta ratkaisu on suojaussalkku, joka maksimoi\nerotuksen voittoa/tappiota kuvaavan satunnaismuuttujan odotusarvon ja varianssin\nv\u00e4lill\u00e4.\nRatkaisun l\u00f6yt\u00e4miseksi aloitamme kertaamalla t\u00e4rkeit\u00e4 ja tarpeellisia tuloksia todenn\u00e4k\u00f6isyysteoriasta ja stokastisesta analyysist\u00e4. T\u00e4m\u00e4n j\u00e4lkeen esittelemme lyhyesti\nmoninkertaiset stokastiset integraalit ja niiden ominaisuuksia sek\u00e4 k\u00e4yt\u00e4mme n\u00e4it\u00e4 Malliavin derivaatan m\u00e4\u00e4rittelyyn. Odotusarvo-varianssi -ongelman ratkaisun l\u00f6yt\u00e4miseksi k\u00e4yt\u00e4mme \"Linear-Quadratic\" -teoriaa. Oletamme apuongelman ja osoitamme,\nett\u00e4 ratkaisemalla apuongelman on mahdollista ratkaista my\u00f6s alkuper\u00e4inen\nongelma. K\u00e4ytt\u00e4m\u00e4mme \"Linear-Quadratic\" -teoria on yhteydess\u00e4 takaperoisiin stokastisiin\ndifferentiaaliyht\u00e4l\u00f6ihin ja tutkielmassa n\u00e4emme n\u00e4iden yhteyden Malliavin\nderivaattaan. Johdamme my\u00f6s eksplisiittiset ratkaisut suoran sopimuksen ja Eurooppalaisen\nmyynti- ja osto-option Malliavin derivaatalle.\nT\u00e4ss\u00e4 tutkielmassa vaateen oletetaan olevan Malliavin derivoituva ja t\u00e4m\u00e4 mahdollistaa\neksplisiittisen ratkaisun l\u00f6yt\u00e4misen. P\u00e4\u00e4teoreemana muotoilemme eksplisiittisen\nsuojaussalkun, joka ratkaisee odotusarvo-varianssi -ongelman tilanteessa, jossa\nsijoitusmarkkina on ep\u00e4t\u00e4ydellinen.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "In this thesis we introduce a mean-variance hedging problem in an incomplete\nmarket. As a main source we follow X. Xue, J. Zhang and C. Weng article Mean-\nvariance Hedging with Basis Risk. We assume a time interval [0; T] for some T > 0,\nan arbitrage free nancial market, and consider one risk-free asset and (m + 1) risky\nassets. The dynamics of the assets are given by stochastic differential equations with\ndeterministic and Borel-measurable coefficients. One risky asset is connected to the\npay-off function which we want to hedge. We assume that this connected asset can not\nbe used in hedging and this makes the market incomplete. Because of incompleteness\nperfect hedging is not possible.\nWe de fine a profi t-and-loss random variable by using the difference between the\nvalue of the hedging portfolio and the pay-off function. A mean-variance criterion is\nused to this random variable and by that the solution is a hedging strategy which\nmaximizes the difference between the expected value and variance of the profi t-and-loss\nrandom variable.\nTo fi nd a solution we start by recalling some important results from probability\ntheory and stochastic analysis. We introduce shortly multiple stochastic integrals\nand properties of them. These integrals are used to de fine the Malliavin derivative.\nThe mean-variance hedging problem is solved by using Linear-Quadratic theory. We\nconsider an auxiliary problem and show that by solving the auxiliary problem we\nare able to solve the original problem. The solving method with Linear-Quadratic\ntheory is connected to the backward stochastic differential equations (BSDE) and in\nthe thesis we see also the connection of the BSDEs to the Malliavin derivative. We\ncompute an explicit formula for the Malliavin derivative of a forward contract and an\nEuropean put and call option.\nThe pay-off function in this thesis is assumed to be Malliavin differentiable and\nhence we are able to give an explicit solution for the problem. As a main theorem\nwe formulate an explicit hedging strategy which solves the mean-variance hedging\nproblem in the incomplete market.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2021-10-04T09:46:43Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2021-10-04T09:46:43Z (GMT). No. of bitstreams: 0\n Previous issue date: 2021", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "56", "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": "hedging", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "incomplete market", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Malliavin calculus", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "backward stochastic differential equations", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "About mean-variance hedging with basis risk", "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-202110045057", "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": 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