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Method for Teaching Probability Theory in Financial Engineering: Connecting with High School Mathematics

Author

Listed:
  • Yukari Shirota
  • Tetsuji Kuboyama

Abstract

本稿では，大学における金融工学数学における確率の学習と，高校数学における確率の学習の関連を示す。金融工学数学の確率論の初歩が，数学Aの範囲の確率論の知識で十分理解可能であることを示す。その例としてオプションの理論における株価の二項モデルを示す。次に，数学Aでの確率論の教え方の改善について述べる。金融工学数学の中で，確率論は非常に重要である。しかしながら学生に確率の定義にある，同様に確からしい，の意味を教えることは容易ではない。順列の確率問題よりも，組合せの確率問題のほうが学生は困難を感じるようである。そこで，組合せの確率問題において，同様に確からしいサンプルの空間を，学生が容易にイメージできるようにする教授法を考案したので，本稿で提案する。サイコロや球を，識別子付きオブジェクトとして並べ，いずれのオブジェクトも同じ値域をもつようにモデル化する。この教授法をオブジェクト等確率モデル法と呼ぶ。本稿では，オブジェクト等確率モデル法により，組合せの確率問題の同様に確からしいサンプルの空間が，容易にイメージできることを示す。

Suggested Citation

  • Yukari Shirota & Tetsuji Kuboyama, 2010. "Method for Teaching Probability Theory in Financial Engineering: Connecting with High School Mathematics," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 47(3), pages 151-161.
    • Handle: RePEc:abc:gakuep:47-3-2
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