オプション取引の逆正弦法とブラウン運動

最近オプション取引の利益分配を考えながら逆正弦法の事を味わった。
The relationship of this rule to Stirling's approximation and it's usefulness in determining the fraction of the year a trader spends in the black is unclear, but most of the mathematics seem to be correctly derived.
離散と連続の関数で述べられます。the discrete form is in terms of a selection expression, which thus involves factorials. Stirling's approximation is an approximation for n!.
However, the derivation of "Lemma 2", a necessary step in the EliteTrader.com paper I read, is unclear. Proving P(2k seconds in black Over 2n total seconds) = u2k*u(2n-2k) is difficult. In fact, this was verified not through conceptual reasoning but through standard induction on both n and k. Begin with the assumption that P0,0=u0*u0, which is clearly true. Then, solving for the first of two terms in the k induction is possible and, assuming the k induction holds in the first term of the n induction, the n induction holds and can be used to solve the second term of the k induction. This reasoning is somewhat tenuous, but in fact the P values I the n induction have both k and n values less than or equal to 2k and 2n.
「逆正弦」と言う名前の由来は累積分布関数です。
Based on P(2k,2n)=u(2k)u(2n-2k) and u(2n)=(1/2^2n)choose(2n,n), the formula of (1/pi)(1/n)(1/sqrt(t(1-t))) is obtained for P(2k,2n)
This approach validates the Arcsine Law for discrete Bernoulli-distributed outcomes, but a separate proof for normally-distributed outcomes is required.
ベルヌーイ分布より正規分布の場合の証明が大切です。