Then, an exact and explicit solution for American options on a dividend-paying stock is derived as a Maclaurin series. Meanwhile, the corresponding optimal early exercise boundary is also obtained in a closed-form solution. As the solutions are in series expansion, an auxiliary parameter is ...
Translations are mine (including from Maclaurin and De Morgan, retranslated from Lajugie’s and Boyé’s French citations). This excursion was spurred by a side remark in the article How to Take Advantage of the Blur Between the Finite and the Infinite by the recently deceased mathematician ...
Then, an exact and explicit solution for American options on a dividend-paying stock is derived as a Maclaurin series. In addition, the corresponding optimal early exercise boundary and the Greeks are obtained in closed-form solutions. A nonlinear sequence transformation, the Pad茅 technique, is ...
If the quotient of the pseudo-composite functions in Theorem 4.1 is smooth, then the coefficients of its Taylor/Maclaurin series can also be expressed in terms of a sum over the partitions. In a second corollary the theory is extended by taking an arbitrary power 蟻 of the quotient of the...
A higher order approximation is developed based on the MacLaurin series of the moments of the performance measures. A novel interpolation approximation is proposed which combines the heavy traffic limits and any number of the light traffic derivatives using the theory of multipoint Pade approximation....
Using the Maclaurin formula, 𝑓(𝜌)f(ρ) can be extended. After disregarding the terms of third and higher orders, we have: ln(𝑄𝐴)=𝑢0+𝑢1⋅ln(𝑄𝑉𝐴)+𝑢2⋅ln(𝑄𝐼𝑁𝑇𝐴)+𝑢3⋅[ln(𝑄𝑉𝐴/𝑄𝐼𝑁𝑇𝐴)]2+𝜀ln(QA)=u0+u1⋅ln(QVA...