Description: This is a Fellowship Credit Research Paper. A portfolio of different insurance policies such as temporary, endowment and whole-life insurance policies is studied in a stochastic mortality and interest environment. The first two moments of the present value of the benefits of the portfolio are derived. The riskiness of the portfolio as measured by the variance of the present value of the benefits can be divided into an insurance risk and an investment risk in two different ways. One way leads to a more natural interpretation of the two risk components. A simple portfolio is used to illustrate the results.

Description: In this paper we discuss the link between the price of a contingent claim and its replicating strategies. We compute the replicating strategies for some contingent claims when the price of stocks are modeled using either the Wiener process or the Poisson process. These replicating strategies are essential knowledge if one wishes to implement a dynamic trading strategy.

Description: Traditional mean-variance method does not take skewness of the random rate of return into consideration. It only considers minimum variance for a given acceptable rate of return, which limited the probability of obtaining higher rate of return. If the skewness of return for the portfolio is incorporated into model of traditional approach, then the resulting non-linear programing model is not computational efficient, which certainly is complicated. On the other hand, possibilistic programming provides more efficient techniques to solve the imprecision nature of rate of return and also preserves the original linear model.

Description: Applications of Lagrangian distributions to modelling claim frequency data in an insurance portfolio is a relatively new concept. The major difficulty is that the generating functions of these distributions cannot be expressed in terms of elementary functions. Also deriving moments and/or cumulants is somewhat tedious. This article illustrates how to use Maple effectively to overcome these difficulties.