# zbMATH — the first resource for mathematics

Valuation of equity-indexed annuity under jump diffusion process. (English) Zbl 1199.91094
Summary: The equity-indexed annuity (EIA) contract offers a proportional participation in the return on a specified equity index, in addition to a guaranteed return on the single premium. In general, in valuation of equity-indexed annuity, it is often assumed that the equity index is within the Black-Scholes framework, but some rare events (release of an unexpected economic figure, major political changes or even a natural disaster in a major economy) can lead to brusque variations in prices. So in the present work we study the equity index following a jump diffusion process. By Esscher transform, we obtain a closed form of the valuation of point-to-point EIA, which can be expressed as a function of some pricing factors. Finally, we conduct several numerical experiments in which the break even participation rate $$\alpha$$ can be solved when the other factors are fixed. The relationship between $$\alpha$$ and the other factors are also discussed.
##### MSC:
 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics