Markovian Annuities and Insurances

Traditionally, properly and casualty products have been thought of as "short duration contracts", while life insurance products have been thought of as "long duration contracts". Many modern property and casualty products have risk profiles and cash flow characteristics that are more akin to life insurance than to traditional property and casualty lines. In this paper, using bond insurance as a primary example, we show how such products can be priced and reserved using techniques from the capital markets and from life insurance. The "'life reserves" held by life companies are essential premium deficiency reserves in that they are required not to pay losses that have occurred, but rather to make up the shortfall in future premium collections. Since bond insurance is so similar to life insurance, it is no surprise that the appropriate reserves for bond insurers are also premium deficiency reserves.