2002 Fiscal Year Annual Research Report

デリバテイブ価格計算のための超一様分布列の構成に関する研究

Research Project

Project/Area Number	13558046
Research Institution	University of Tsukuba
Principal Investigator	藤原良叔筑波大学, 社会工学系, 教授 (30165443)
Co-Investigator(Kenkyū-buntansha)	神保雅一慶応大学, 理工学部, 教授 (50103049) 岸本一男筑波大学, 社会工学系, 教授 (90136127) 繆いん筑波大学, 社会工学系, 講師 (10302382) 手塚集日本IBM基礎研究所, 研究員栗木進二大阪府立大学, 大学院・工学研究科, 助教授 (00167389)
Keywords	超一様分布列 / (T, M, S)-net / (T, S)-sequence / Teta-configuration / derandomization / i-binomial property / nested design / Difference set
Research Abstract	金融工学でオプション価格を計算する時,超多次元で積分をする必要がある.一般に次元が大きいのでモンテカルロ法による数値積分を行なう.普通疑似乱数を用いるが、普通の乱数を使うより組合せ的にバランスした乱数列を使う方が精度が格段に良くなることが理論的に証明されている.これを準モンテカルロ法といい,(t, m, s)-netあるいは(t, s)-sequenceと呼ばれる超一様分布列と呼ばれる組み合わせ的乱数列を使う。また各種の実験でもこの(t, m, S)-netや(t, s)-sequenceを使うと精度が高まることが認められている。今年度は藤原・ミャオによって(t, m, s)-netがt=4以下ではTheta-Configurationと同値であることを示した.またt一般的にTheta-Configurationを再帰的に定義した. 手塚は最近提案されたHickernell列と呼ばれる超一様分布列について、その類似なものを有限体上の多項式を使つて定義し、それが(t, s)-Sequenceを構成することを示した。つぎに,(t, s)-sequenceのなかで最も一様なのが(O, s)-sequenceである。現在は、そのパラメーターをランダムに選んで使っているが、手塚は、いいパラメーターのみを探し出す方法を考察した。いいパラメーターが見つかってしまうと「ランダム性」が必要なくなるため、この手続きをDerandomizationと呼んでいる。またひとつのアプローチとして、i-binomial propertyと呼ばれる性質を利用することを提案した。また(t, m, s)-netの構成の基礎理論に関連するNested designやDifference setに関する研究でいくつか結果がでた.

Research Products

(14 results)

All Other

All Publications (14 results)

[Publications] R.Fuji-Hama, Y.Miao: "A Note on Geometrical Structures of Linear Ordered Orthogonal Arrays and (T, M, S)-net of Low Strength"Deaign, Code and Cryptographs. 26. 257-263 (2002)
[Publications] R.Fuji-Hara, Y Miao, S.Shinohara: "Complete set of disjoint difference families and their applications"Journal of Statistical Planning and Inference. 106. 87-103 (2002)
[Publications] R.Fuji-Hara, S.Kuriki, Y.Miao, S.Shinohara: "Balanced nested designs and balanced n-ary designs"Journal of Statistical Planning and Inference. 106. 57-67 (2002)
[Publications] R.Fuji-Hara, S.Kageyama, S.Kuriki, Y.Miao, S.Shinohara: "Balanced nested designs and balanced arrays"Discrete Mathematics. 259. 91-119 (2002)
[Publications] Y.Chang, R.Fuji-Hara, Y.Miao: "Combinatorial Constructions of Optimal Optical Orthogonal Codes with Weight"IEEE transaction of Information Theory. (to appear).
[Publications] Y.Chang, Y.Miao: "General constructions for double group divisible designs and double frames"Designs, Codes and Cryptography. 26. 155-168 (2002)
[Publications] S.Furino, S.Kageyama, A.C.H.Ling, Y.Miao, J.Yin: "Frames with block size four and index three"Journal of Statistical Planning and Inference. 106. 117-124 (2002)
[Publications] S.Tezuka: "On Derandomization of Randomized (O, s)-sequences"Proc of Foundation of Computational Mathematics. 35-36 (2002)
[Publications] S.Tezuka: "Toward Derandomization of Owen's Random Scrambling"Dagstuhl Seminar on Algorithm and Complexity for Continuous Promblem. 17 (2002)
[Publications] S.Tezuka: "Polynomial Arithmetic Analogue of Hickernell Sequences"Proc.Monte Carlo and Quasi-Monte Carlo Methods. 43 (2002)
[Publications] Y.Mutoh, T.Morihara, M.Jimbo: "The exsitence of 2x4 grid designs and their applications"SIAM Discrete Mathematics. (to appear).
[Publications] H.L.Fu, F.K.Hwang, M.Jimbo, Y.Mutoh, C.L.Shiue: "Decomposing Complete Graphs into K_rxK_c's"J.Statist.Plann.Inference. (to appear).
[Publications] T.Adachi, M.Jimbo, S.Kageyama: "Combinatorial structure of group divisible designs without α-resolution classes in each group"Discrete Math. (to appear).
[Publications] 手塚集: "ウォール街を動かすソフトウエア"岩波書店. 110 (2002)

2002 Fiscal Year Annual Research Report

デリバテイブ価格計算のための超一様分布列の構成に関する研究

Principal Investigator

藤原 良叔 筑波大学, 社会工学系, 教授 (30165443)

Research Products

[Publications] R.Fuji-Hama, Y.Miao: "A Note on Geometrical Structures of Linear Ordered Orthogonal Arrays and (T, M, S)-net of Low Strength"Deaign, Code and Cryptographs. 26. 257-263 (2002)

[Publications] R.Fuji-Hara, Y Miao, S.Shinohara: "Complete set of disjoint difference families and their applications"Journal of Statistical Planning and Inference. 106. 87-103 (2002)

[Publications] R.Fuji-Hara, S.Kuriki, Y.Miao, S.Shinohara: "Balanced nested designs and balanced n-ary designs"Journal of Statistical Planning and Inference. 106. 57-67 (2002)

[Publications] R.Fuji-Hara, S.Kageyama, S.Kuriki, Y.Miao, S.Shinohara: "Balanced nested designs and balanced arrays"Discrete Mathematics. 259. 91-119 (2002)

[Publications] Y.Chang, R.Fuji-Hara, Y.Miao: "Combinatorial Constructions of Optimal Optical Orthogonal Codes with Weight"IEEE transaction of Information Theory. (to appear).

[Publications] Y.Chang, Y.Miao: "General constructions for double group divisible designs and double frames"Designs, Codes and Cryptography. 26. 155-168 (2002)

[Publications] S.Furino, S.Kageyama, A.C.H.Ling, Y.Miao, J.Yin: "Frames with block size four and index three"Journal of Statistical Planning and Inference. 106. 117-124 (2002)

[Publications] S.Tezuka: "On Derandomization of Randomized (O, s)-sequences"Proc of Foundation of Computational Mathematics. 35-36 (2002)

[Publications] S.Tezuka: "Toward Derandomization of Owen's Random Scrambling"Dagstuhl Seminar on Algorithm and Complexity for Continuous Promblem. 17 (2002)

[Publications] S.Tezuka: "Polynomial Arithmetic Analogue of Hickernell Sequences"Proc.Monte Carlo and Quasi-Monte Carlo Methods. 43 (2002)

[Publications] Y.Mutoh, T.Morihara, M.Jimbo: "The exsitence of 2x4 grid designs and their applications"SIAM Discrete Mathematics. (to appear).

[Publications] H.L.Fu, F.K.Hwang, M.Jimbo, Y.Mutoh, C.L.Shiue: "Decomposing Complete Graphs into K_rxK_c's"J.Statist.Plann.Inference. (to appear).

[Publications] T.Adachi, M.Jimbo, S.Kageyama: "Combinatorial structure of group divisible designs without α-resolution classes in each group"Discrete Math. (to appear).

[Publications] 手塚 集: "ウォール街を動かすソフトウエア"岩波書店. 110 (2002)

藤原良叔筑波大学, 社会工学系, 教授 (30165443)

[Publications] 手塚集: "ウォール街を動かすソフトウエア"岩波書店. 110 (2002)