Description: This paper illustrates the application of stochastic control methods in managing the risk associated with an insurance business. We present the Hamilton-Jacobi-Bellman HJB equation and demonstrate its use in finding the optimal investment strategy based on some given criteria. Here we consider an insurance business with a fixed amount available for investment in a portfolio consisting of one non-risky asset and one risky asset. The object of the resulting control problem is to determine the investment strategy that minimizes infinite time ruin probability. The existence of a solution to the resulting HJB equation is shown. The relevant verification lemma is not presented in this paper and a numerical algorithm is given instead. Examples applied to exponential claims are also presented.

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: Discussion of the movement toward principle-based reserves for LTC insurance.

Description: The research investigates the challenges associated with determining a “fair value” assessment for embedded options in two product types and incorporates the process into product pricing and liability valuation

Description: In this paper, we derive three important longevity Greeks on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility.

Description: The article describes the key components of actuarial model, leading practices in designing them, and characteristics of well-built models.

Description: The article warns against treating the results of a stochastic model with more deference than other actuarial analysis, and describes some hidden risks involved with choice of model and calibration.

Description: Are Your Scenarios on Target?From Risks and Rewards Newsletter, August 2005, Issue No. 47. Actuaries are faced with the dilemma of how to incorporate advances in insurance products and modeling technology into their work. Increasingly, this means looking at a large number of potential outcomes using stochastic simulations.

Description: Describes using the new multi-risk scenario generator to create sensitivity tests at moderately adverse probability levels, resulting in margins to use for PBR.

Description: This article explains why stochastic modeling is becoming more pervasive, and describes a specific stochastic application with metrics to measure results.