Longevity-linked derivatives are one of the most important longevity risk management solutions for pension schemes and life annuity portfolios. In this paper, we decompose several derivatives—such as geared bonds longevity-spread bonds—into portfolios involving options. For instance, show that fair value an index-based swap can be broken down into a portfolio long short positions in European-st...

The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized spatial filtering systems: Several filters...