*Tid:***10 januari 2005 kl 1515-1600 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Olof Werneman.
**

**Titel:** **
Pricing Lifelong Joint Annuity Insurances and Survival Annuity Insurances
Using Copula Modeling of Bivariate Survival.
(Examensarbete)
**

* Sammanfattning: *
This thesis investigates the dependence in survival of married couples and
its effect on the pricing of lifelong joint annuity insurances and survival
annuity insurances. The dataset used contained 199127 observations of
married couples where both husband and wife reached the age of 61 or more
and the maximum difference in age between husband and wife was ten years.
The Makeham distribution is proved to be a very good choice to model the
marginal distributions. The hypothesis of independent survival for married
couples is rejected at all reasonable levels of significance. The data show
a weak positive dependence. The dependence structure is shown to best fit a
Clayton copula model. For the lifelong joint annuity insurance the Clayton
copula-model yields 1.6% lower discounted expected future payments than,
when assuming independence. When pricing a survival annuity insurance it is
important to distinguish between the case when the husband is insured and
wife is co-insured and the case when the wife is insured and the husband is
co-insured. If the ages of the husband and wife are approximately equal the
Clayton copula-model yields 8% lower discounted expected future payments in
the first case and 10% lower in the second case. In the first case, the
difference expressed as a percentage, between the discounted expected future
payments of the Clayton copula-model and the independent model is decreasing
as the difference in age increases from -10 to 10. In the second case the
difference expressed as a percentage is increasing.