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甲魚日記 - 2026/01/18 讀完BM和GBM與他們的快樂小夥伴 豪想哭 | Penana
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甲魚日記
ISSUE #2
Author: 栩栩
Published:
Jan 18, 2026
甲魚日記
Author: 栩栩
Published:
Jan 18, 2026
ISSUE #2
2026/01/18 讀完BM和GBM與他們的快樂小夥伴 豪想哭
No Plagiarism!i37uuiiPRo7iOj8PVyLlposted on PＥNAＮＡ

Rrrrrrrrr念完第三章了，可是習題都不會寫我完蛋了。

話說我跳過前兩章的Probability Theory和Normal Distribution是不是個很糟糕的決定啊，還以為自己統計基礎不錯，終究是大意了。

心路歷程如下：

3.1  Brownian Motion

讚哦，數學與物理學(aka應用數學)聯合起來攻打金融的傑出一手

3.2 Brownian Motion as a Limit of Simpler Models

模型可愛捏

3.3 Geometric Brownian Motion

因為不想算BM的負數把它塞進exp和ln裡，詭異的數學人和物理人

終於發現有些人寫log其實是在表示ln

3.4 The Maximum Variable

這是在找路徑裡面的最大值的，通常是看它有沒有超過某個特定值y

然後這裡的鏡像真的順了超級久

Theorem 3.4.1 有夠難證明54Please respect copyright.ＰＥＮＡＮＡ84QN4Kilil

它在算已知終點條件X(t)=x下，最大值M(t)>y的條件機率

Corollary 3.4.1 更加不妙，直接按skip鍵跳過

(順便把我寫習題的正確性也按skip跳過)

3.5 The Cameron-Martin Theorem

a special case of Girsonav's theorem

再次跳過證明ww

不過解釋一下功用54Please respect copyright.ＰＥＮＡＮＡzIMxb9SAYW

是把有drift的BM(用乘上一個weight的方式)，轉換到沒有drift的BM

沒有drift的BM因為有對稱性比較好算

但是我依然想說，數學家和應用數學家們對"好算"的標準有點太低落了

總結

3.4跟3.5都好軟爛，然後得把前兩章補起來，好討厭統計Rrrrrrr

以後就在這裡寫完金融數學導論的前半本心得

應該會寫到Black-Scholes model為止，有整個寒假我可以的吧

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216.73.217.39

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甲魚日記
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Last updated: Jan 18, 2026
Total word count: 517
Total reading time: 2 Minutes
Writer:
栩栩
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