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KAKEN_15K04936seika.pdf
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Download
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:165.3 KB
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:Oct 31, 2019 |
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Total downloads since Oct 31, 2019 : 612
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Malliavin解析による最適ヘッジ戦略の導出とその数値計算法の研究
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Malliavin カイセキ ニ ヨル サイテキ ヘッジ センリャク ノ ドウシュツ ト ソノ スウチ ケイサンホウ ノ ケンキュウ
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Malliavin kaiseki ni yoru saiteki hejji senryaku no dōshutsu to sono sūchi keisanhō no kenkyū
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Research on mathematical expressions and numerical methods for optimal hedging strategies via Malliavin calculus
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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 (三田) ・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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2019
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科学研究費補助金研究成果報告書
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2018
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| Abstract |
ジャンプ型確率過程によって記述される非完備市場を考え、2つの最適ヘッジ戦略local risk-minimizing(LRM)とmean-variance hedging(MVH)に対し、Malliavin解析を用いてそれらの表現及び数値計算法の開発を目指した。とりわけ、(1)BNSモデルに対するLRMの導出と数値計算、(2)指数型加法過程モデルに対するMVHの表現の導出と数値計算、(3)normal inverse Gaussian過程モデルに対するLRMとMVHの数値計算、及び(4)BNSモデルに対するVIXオプションのLRMの表現と数値計算に関する研究を行った。
Considering incomplete markets described by a jump type stochastic process, we aimed to derive, using Malliavin calculus, mathematical expressions of two optimal hedging strategies : local risk-minimizing (LRM) and mean-variance hedging (MVH) strategies; and to develop numerical methods for them. We have solved the following problems: (1) mathematical expressions and numerical methods of LRM strategies for BNS models, (2) expressions and numerical methods of MVH strategies for exponential additive models, (3) computation on LRM and MVH for normal inverse Gaussian models, and (4) expressions and numerical methods of LRM strategies for VIX options for BNS models.
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研究種目 : 基盤研究 (C) (一般)
研究期間 : 2015～2018
課題番号 : 15K04936
研究分野 : 解析学基礎
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