2001 Fiscal Year Annual Research Report

デリバティ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)	神保雅一慶應義塾大学, 理工学部, 教授 (50103049) 岸本一男筑波大学, 社会工学系, 教授 (90136127) ミャオイン筑波大学, 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	オプション価格 / 準モンテカルロ法 / (T,M,S)-net / 有限射影幾何 / Theta-Configureation / (t,s)-sequence / 高次元積分 / スクランブル法
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最近理論的に証明された。これを準モンテカルロ法といい,(T,M,S)-net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を使うと精度が高まることが認められている。今年度は,T=3,4のとき,この(T,M,S)-netを有限射影幾何上でTheta-Configureationと呼ぶ幾何構造を定義し,それが(T,M,S)-netと同値であることを証明した。T=3のとき,強さ3の直交配列と同値であることを証明した。またT=4のときはTwisted Cubicと呼ばれる代数曲線からTheta-Configureationが構成できることを証明した。この結果は学術雑誌に投稿し採択された。準モンテカルロ法の理論と実践の現状についてサーベイをした。まず,モンテカルロ法高速化に関する研究の重要な方向について議論する。次に,準モンテカルロ法の高次元積分問題への適用についての現状を述べた。これらを論文にして国際会議で報告し,報告集に掲載された。また,(T,M,S)-netを系列化した(t,s)-sequenceの研究を行った。(t,s)-sequenceの新しいスクランブル法について研究した。その金融問題への適用とその有効性について報告した。また本方式による実効次元探索についても述べる。これらを論文にして国際会議で報告し,報告集に掲載された。その他,間接的に(T,M,S)-netの構成に関係する各種の組合せ的デザイン理論の基礎研究を行い,各種の学術雑誌に掲載された。

Research Products

(21 results)

All Other

All Publications (21 results)

[Publications] R.Fuji-Hara, Y.Miao and J.Yin: "Optimal(9v,4,1) optical orthogonal codes with v a product of primes congruent to 1 modulo 4"SIAM Journal on Discrete Mathematics. Vol.14. 256-266 (2001)
[Publications] R.Fuji-Hara, Y.Miao, J.Wang and J.Yin: "Directed B(K,1;v) with K-{4,5} and {4,6} Related to Deletion/Insertion-Correcting Codes"Journal of Combinatorial Designs. Vol.9. 147-156 (2001)
[Publications] R.Fuji-Hara, Y.Miao and S.Shinohara: "Complete Set of disjoint difference families and their applications,"Journal of Statistical Planning and Influence. (掲載予定).
[Publications] R.Fuji-Hara, S.Kuriki, Y.Miao and S.Shinohara: "Balanced nested designs and balanced n-ary designs"Journal of Statistical Planning and Influence. (掲載予定).
[Publications] R.Fuji-Hara and Y.Miao: "A note on a geometrical construction of (t,m,s)-net and ordered orthogonal arrays"Journal of Codes,Design and Cryptograph. (掲載予定).
[Publications] R.Fuji-Hara, S.Kageyama, S.Kuriki, Y.Miao and S.Shinohara: "Balanced Nested designs and Balanced Arrays"Discrete Mathematics. (掲載予定).
[Publications] R.J.R.Abel, M.Buratti, M.Greig and Y.Miao: "Constructions for rotational near resolvable block designs"Journal of Combinatorial Designs. 9. 157-181 (2001)
[Publications] R.J.R.Abel, M.Greig, Y.Miao and L.Zhu: "Resolvable BIBDs with block size 7 and index 6"Discrete Mathematics. 226. 1-20 (2001)
[Publications] S.Kageyama and Y.Miao: "Existence of nested designs with block size five"Journal of Statistical Planning and Inference. 94. 249-254 (2001)
[Publications] C.Lam and Y.Miao: "(C+G,K,λ) difference families"Designs,Codes, and Cryptography. 24. 291-304 (2001)
[Publications] C.Lam, Y.Miao and M.Mishima: "Cyclically resolvable cyclic Steiner 2-systems S(2,4,52)"Journal of Statistical Planning and Inference. 95. 245-256 (2001)
[Publications] Y.Chang and Y.Miao: "Constructions for optimal optical orthogonal codes"Discrete Mathematics. (掲載予定).
[Publications] Y.Chang and Y.Miao: "General constructions for double group divisible designs and double frames"Designs,Codes and Cryptography. (掲載予定).
[Publications] T.Hishida, K.Ishikawa, M.Jimbo, S.Kageyama, and S.Kuriki: "Non-existence of a nested BIB design NB(10,15,2,3)"The Journal of Combinatorial Mathematics and Combinatorial Computing. 36. 55-63 (2001)
[Publications] I.Mejza, S.Kuriki and S.Mejza: "Balanced square lattice designs in split-block designs"Colloquium Biometryczne. 31. 97-103 (2001)
[Publications] S.Tezuka: "Quasi-Monte Carlo -- Discrepancy between Theory and Practice"Monte Carlo and Quasi-Monte Carlo Methods 2000,Springer. 124-140 (2002)
[Publications] H.Faure and S.Tezuka: "Another Random Scrambling of Digital(t,s)-Sequences,"Monte Carlo and Quasi-Monte Carlo Methods 2000,Springer. 242-256 (2002)
[Publications] K.Ozawa, M.Jimbo, S.Kageyama and S.Mejza: "Optimality and efficiency of incomplete split-block designs"Metrika. (掲載予定).
[Publications] M.Jimbo and S.Kageyama: "Discrete Structure of Group Divisible Design with r=λ_1+1"ICA Bulletin. 32. 29-38 (2001)
[Publications] T.Adachi, M.Jimbo and S.Kageyama: "Combinatorial structure of group divisible designs without α-resolution classes in each group"Discrete Mathematics. (掲載予定).
[Publications] Y.Mutoh, T.Morihara, M.Jimbo and H.L.Fu: "The existence of 2 x 4 grid designs and its applications"SIAM Journal on Discrete Mathematics. (掲載予定).

2001 Fiscal Year Annual Research Report

デリバティ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-Hara, Y.Miao and J.Yin: "Optimal(9v,4,1) optical orthogonal codes with v a product of primes congruent to 1 modulo 4"SIAM Journal on Discrete Mathematics. Vol.14. 256-266 (2001)

[Publications] R.Fuji-Hara, Y.Miao, J.Wang and J.Yin: "Directed B(K,1;v) with K-{4,5} and {4,6} Related to Deletion/Insertion-Correcting Codes"Journal of Combinatorial Designs. Vol.9. 147-156 (2001)

[Publications] R.Fuji-Hara, Y.Miao and S.Shinohara: "Complete Set of disjoint difference families and their applications,"Journal of Statistical Planning and Influence. (掲載予定).

[Publications] R.Fuji-Hara, S.Kuriki, Y.Miao and S.Shinohara: "Balanced nested designs and balanced n-ary designs"Journal of Statistical Planning and Influence. (掲載予定).

[Publications] R.Fuji-Hara and Y.Miao: "A note on a geometrical construction of (t,m,s)-net and ordered orthogonal arrays"Journal of Codes,Design and Cryptograph. (掲載予定).

[Publications] R.Fuji-Hara, S.Kageyama, S.Kuriki, Y.Miao and S.Shinohara: "Balanced Nested designs and Balanced Arrays"Discrete Mathematics. (掲載予定).

[Publications] R.J.R.Abel, M.Buratti, M.Greig and Y.Miao: "Constructions for rotational near resolvable block designs"Journal of Combinatorial Designs. 9. 157-181 (2001)

[Publications] R.J.R.Abel, M.Greig, Y.Miao and L.Zhu: "Resolvable BIBDs with block size 7 and index 6"Discrete Mathematics. 226. 1-20 (2001)

[Publications] S.Kageyama and Y.Miao: "Existence of nested designs with block size five"Journal of Statistical Planning and Inference. 94. 249-254 (2001)

[Publications] C.Lam and Y.Miao: "(C+G,K,λ) difference families"Designs,Codes, and Cryptography. 24. 291-304 (2001)

[Publications] C.Lam, Y.Miao and M.Mishima: "Cyclically resolvable cyclic Steiner 2-systems S(2,4,52)"Journal of Statistical Planning and Inference. 95. 245-256 (2001)

[Publications] Y.Chang and Y.Miao: "Constructions for optimal optical orthogonal codes"Discrete Mathematics. (掲載予定).

[Publications] Y.Chang and Y.Miao: "General constructions for double group divisible designs and double frames"Designs,Codes and Cryptography. (掲載予定).

[Publications] T.Hishida, K.Ishikawa, M.Jimbo, S.Kageyama, and S.Kuriki: "Non-existence of a nested BIB design NB(10,15,2,3)"The Journal of Combinatorial Mathematics and Combinatorial Computing. 36. 55-63 (2001)

[Publications] I.Mejza, S.Kuriki and S.Mejza: "Balanced square lattice designs in split-block designs"Colloquium Biometryczne. 31. 97-103 (2001)

[Publications] S.Tezuka: "Quasi-Monte Carlo -- Discrepancy between Theory and Practice"Monte Carlo and Quasi-Monte Carlo Methods 2000,Springer. 124-140 (2002)

[Publications] H.Faure and S.Tezuka: "Another Random Scrambling of Digital(t,s)-Sequences,"Monte Carlo and Quasi-Monte Carlo Methods 2000,Springer. 242-256 (2002)

[Publications] K.Ozawa, M.Jimbo, S.Kageyama and S.Mejza: "Optimality and efficiency of incomplete split-block designs"Metrika. (掲載予定).

[Publications] M.Jimbo and S.Kageyama: "Discrete Structure of Group Divisible Design with r=λ_1+1"ICA Bulletin. 32. 29-38 (2001)

[Publications] T.Adachi, M.Jimbo and S.Kageyama: "Combinatorial structure of group divisible designs without α-resolution classes in each group"Discrete Mathematics. (掲載予定).

[Publications] Y.Mutoh, T.Morihara, M.Jimbo and H.L.Fu: "The existence of 2 x 4 grid designs and its applications"SIAM Journal on Discrete Mathematics. (掲載予定).

藤原良叔筑波大学, 社会工学系, 教授 (30165443)