Description: Design and future maintenance of an asset portfolio backing a new line of business is critical for proper asset and liability management for that business. Most portfolio optimization methods utilize linear or quadratic programming and require the user to specify the asset and liability attributes and cash flows into the program. The programmer must also supply an objective function to allow the program to find the optimal asset mix for the associated liabilities. Two problems with this approach are that the liability cash flows are fairly static and that one must frequently rebalance the portfolio. An alternative approach would be to develop a corporate model of both the assets and liabilities and incorporate various economic scenarios as input into the model. Asset strategies would be measured against a specific objective function that is calculated by the corporate model. Unfortunately, the majority of maximization algorithms available are very time consuming, and obtaining a reasonable portfolio mix becomes impractical. This paper overcomes this difficulty by using a very rapid optimization method from the chemical engineering profession called the Floppy Triangle. The paper includes an example of the use of this process to determine an optimal portfolio. It also discusses modifications of the algorithm that is required when the shorting of assets is not permitted.

Description: Random sum models with compound distributions are used extensively in modeling of insurance risks. Unfortunately, the compound distributions themselves are awkward to evaluate. Consequently, various numerical and analytical approximative techniques have been used. In this talk we derive various upper and lower bounds on the tails of compound distributions. Some notions in reliability theory are used.

Description: This paper presents a multi-state stochastic model for analyzing continuing care retirement community CCRC populations. The model considers CCRCs with a number of independent living units and a skilled nursing facility. Residents may transfer temporarily or permanently to this facility. It is assumed that units vacated by deaths, withdrawals or permanent transfers are immediately occupied by new residents. Transfers are modeled using a time-homogeneous Markov process. The paper provides some probabilistic results and some numerical results obtained using this model. Some important generalizations of the model are also briefly discussed.

Description: This review summarizes the key features of a stochastic model that works with non-life insurance claim incurral, accrual and reporting. More specifically it provides an overview of the claim model components, classical parameter estimators, test statistics, and forecast point estimates and error variances. From Actuarial Research Clearing House 1991, VOL. 1.

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.

Description: The main aim of this paper is to apply some of the techniques of modern time series and econometric analysis to analyse investment data in order to better understand the nature of long run relationships in investment series typically used in stochastic investment models. The paper attempts to identify and address fundamental issues that need to be considered before developing a particular stochastic investment model.

Description: The concept of transformed distributions is generalized in this paper. First the concepts of net premium intensity, loaded premium intensity and load generators arc introduced. Then transformed distributions are identified with premium intensity and hence the loaded premium is calculated from transformed distributions. Finally it is shown that this method of premimn calculation is arbitrage free and it incorporates the strengths of the utility approach.

Description: This paper addresses the evaluation of long-term returns when the short interest rate is modeled by a general diffusion process. By deriving the long-term return dynamics and invoking the Feyman-Kac formula, the long-term return is represented as the solution of a partial differential equation. A finite difference method is derived for the valuation of the long-term return. The method could be used for hedging interest rate risk, pricing and managing interest rate derivatives and interest rate sensitive insurance products. Numerical examples are included.

Description: In the present paper, we propose and investigate a numerical method of computing the probability distribution of S. Inversion of the Laplace transform moment generating function is shown to be a better approach than the existing recursive method for find the distribution of sum of several independent random variables. In the continuous case, in many situations, numerical inversion needs to be used to compute the probability distribution function of the sum.

Description: One of the most important problems in Finance is the valuation of financial securities written on underlying assets whose prices are subject to uncertainty. This paper presents a technique to estimate the unknown stochastic volatilities by solving the inverse problem associated with the parabolic partial differential equation governing risk neutral derivative security prices. This technique can be applied in a very general multi-factor setting and numerical examples are provided.