Description: The series expansion of a probability density function, known to actuaries by Esscher's name and to statisticians as the saddlepoint approximation, typically gets integrated to approximate probability values under the density, with a location parameter in the expansion chosen to optimize convergence of the integrated series. We review the general form, the accuracy and the derivation of the Esscher approximation. Then we propose using related series expansions for the derivative of a probability density function to approximate the value of the point of maximum likelihood for the density. The key is to make the value of the location parameter an unknown and assume it to be the point of maximum likelihood, which leads to a tractable optimization problem to find its value.

Description: One of the first projects undertaken by Claim Analytics was to create a model to predict return to work for group insurance claimants with long term disabilities. This report, sponsored in part by the Society of Actuaries Health Section , is a case study on creating such a model.

Description: The subject of this paper is a financial model for pension planning purposes. The focus of the model is from an individual's point of view with the idea to assist him/her in planning for a financially secure retirement income. The model is dynamic and stochastic, operates in nominal and real terms, and goes beyond the age of retirement. From Actuarial Research Clearing House 1981, Vol. 1.

Description: This paper discusses an example showing how simulation has been used to develop financial projections for variable life insurance with a guaranteed minimum death benefit and how recourse to mathematical analysis based on risk-theoretic considerations can enable us to see the impact of stock price changes more clearly. These projections reveal the effects of stock price fluctuations interacting with the more common elements, such as mortality and persistency, on the financial results of a variable life insurance operation.

Description: The goal of this paper is to dispel the prevailing belief that American-style options cannot be valued efficiently in a simulation model by presenting a general algorithm for such valuation, and thus remove what has been considered a major impediment to the use of simulation models for valuing financial instruments. Discussions of this paper are included.

Description: Equity-indexed annuities [EIAs] can be viewed as mutual funds wrapped around with various guarantees. A recent paper derived a closed form formula for pricing this dynamic guarantee if early withdrawal from the fund [before maturity] is not permitted. This paper studies the pricing of dynamic protection without a maturity date, i.e., the investor chooses the date to cash in the fund accumulation.

Description: The Society of Actuaries seeks to provide actuaries of life insurance companies with a systematic approach for estimating the adverse effects of economic developments that could impede insurer performance. The performance measurements include 1. Return on Equity, 2. Return on Assets, and 3. Increase in Surplus and Capial. Toward that end, this study combines market and economic factors with insurer-specific data to form dynamic financial models of life insurers. Empirical analysis is based on annual data from 1985 through 1995 for 1,593 life insurers. By identifying important exogenous and insurer-specific factors related to life insurer performance, this study provides a basis for actuaries to build dynamic financial models for individual insurers. The study also identifies and describes several web sites that provide access to relevant economic and financial data. Also see the SOA website research page for excel spread sheets that have the charts that should be inserted in this report