Description: In addition to death and maturity guarantees on the mutual funds they sell, some insurance companies make it possible for the investor to extend the guarantees for a fixed number of years. In this paper, we consider the case when that option is of the European type that is, the investor, at maturity, can either close out the contract or extend it for the stated, fixed term. When extended, the guarantee is on the value of the fund at the original maturity date. The fund is assumed to be fully invested in common stock.

Description: This paper presents an approach to analyzing continuing care retirement community [CCRC] data, and demonstrates the methods using data from a large CCRC. It is assumed that residents make transitions among a number of states that represent the levels of care required by residents. There is randomness associated with both the transition times and the states entered at these times. The model is conveniently characterized in terms of transition intensity functions, which represent the instantaneous rates of transition between pairs of states.

Description: Given a financial transaction we are often interested in the number of internal rates of return [yield rates] and their location. From an actuarial point of view, the fundamental question is to identify those transactions with a single yield rate, or a single rate in some interval such as the positive reals. In this paper we are concerned with this counting problem. We survey various results concerning this problem, and provide a unifying approach together with some new insights.

Description: The amount of 1 [i.e., the amount that $ 1 is worth after 1 year] for an account earning a nominal interest r compounded n times annually is Pn[r,t], where t = [t1, . . . ,tn]. Note that Pn[r,t] is a polynomial in r of degree n. Now suppose that the n compounding periods have lengths T1, . . . ,Tn chosen at random. What can we say about Pn[r , T] , where T=[T1, . . . , Tn]? This depends of course on what is meant by choosing random lengths and we will consider two different natural possibilities that give rise to different answers to this question.