Esscher transform ~ INDAHNYA BERBAGI

Jumat, 13 Juni 2014

In actuarial science, the Esscher transform (Gerber & Shiu 1994) is a transform that takes a probability density f(x) and transforms it to a new probability density f(x; h) with a parameter h. It was introduced by F. Esscher in 1932 (Esscher 1932).

Let f(x) be a probability density. Its Esscher transform is defined as

f(x;h)=\frac{e^{hx}f(x)}{\int_{-\infty}^\infty e^{hx} f(x) dx}.\,

More generally, if μ is a probability measure, the Esscher transform of μ is a new probability measure E_h(μ) which has density

\frac{e^{hx}}{\int_{-\infty}^\infty e^{hx} d\mu(x)}

with respect to μ.

Sumber : http://en.wikipedia.org/wiki/Esscher_transform

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