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KAKEN_22540149seika.pdf
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Download
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:105.1 KB
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:Dec 11, 2014 |
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Total downloads since Dec 11, 2014 : 822
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| Title |
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ヘッジを考慮した凸リスク測度による価格付け理論と関連する確率過程論の研究
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| Kana |
ヘッジ オ コウリョ シタ トツリスク ソクド ニ ヨル カカクズケ リロン ト カンレンスル カクリツ カテイロン ノ ケンキュウ
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Hejji o koryo shita totsurisuku sokudo ni yoru kakakuzuke riron to kanrensuru kakuritsu kateiron no kenkyu
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Research on pricing theory by convex risk measures taking account of hedging, and its related stochastic analysis
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新井, 拓児
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アライ, タクジ
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Arai, Takuji
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慶應義塾大学・経済学部・教授
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Research team head
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科研費研究者番号 : 20349830
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2014
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科学研究費補助金研究成果報告書
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2013
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アメリカンオプションに対するショートフォールリスクを考えるため、確率過程上の凸リスク測度の研究を行った。特に、確率過程の最大値がOrlicz空間に入るような空間を導入し、凸リスク測度の表現定理を導出した。次に、凸リスク測度とgood deal boundの関係について研究した。市場が凸錘であるときに、(1) superhedging costの諸性質、(2) 凸リスク測度があるgood deal boundの上下限を与えることとrisk indifference priceであることの同値性、(3) 価格付け理論の基本定理の拡張、について調べた。さらに、市場が単に凸である場合へ拡張した。
I have studied convex risk measures on stochastic processes in order to deal with shortfall risk measures for American options. In particular, I introduced spaces of stochastic processes whose maximum belongs to an Orlicz space; and obtained representation results for convex risk measures defined on such spaces. Next, I have researched on relationship between convex risk measures and good deal bounds. Supposing the market is a convex cone, I investigated (1) properties of superhedging cost, (2) the equivalence for a convex risk measure between that it represent upper and lower bounds of a good deal bound and that it is given as a risk indifference price, (3) extensions of the fundamental theorem of asset pricing. In addition, I extended the above results to the case where the market is merely convex.
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研究種目 : 基盤研究(C)
研究期間 : 2010～2013
課題番号 : 22540149
研究分野 : 数物系科学
科研費の分科・細目 : 数学・数学一般(含確率論・統計数学)
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