Description: Stochastic approximation is a powerful tool for sequential estimation of zero points of a function. In this paper, this methodology is defined and is shown to be related to a broad class of credibility formulae derived for the Exponential Dispersion Family. The authors further consider a Location Dispersion Family which is rich enough and for which no simple credibility formula exists. For this case, a Generalized Sequential Credibility Formula is suggested and an optimal stepwise gain sequence is derived.

Description: The direct and indirect effects of the pandemic have impacted many actuaries’ work since the spring of 2020. This article addresses three considerations actuaries should account for when using risk evaluation models which are focused on projecting remote, highly unlikely losses: model effectiveness, asset risk, and insurance (mortality and mortality) risk.

Description: This paper discusses some of the models used to quantify risk, note some areas where improvements in standard methods are needed, and in some cases suggest alternative approaches for risks in Property and Casualty Insurance and Life Insurance.

Description: 2011 SOA Enterprise Risk Management Symposium, Chicago. This paper suggests the use of a policy event-based loss estimation method using expert input and simulation for forecasting long duration expenditures: that is to say, there is an efficient time, which is random and observable to replace a physical asset.

Description: This is the User's Guide that accompanies the Inflation Generator Excel spreadsheet which is associated with the research report entitled 'The Effect of Deflation or High Inflation on the Insurance Industry.'

Description: Commentary on practical observations resulting from constructing and running Economic Capital models. Possible standardization of assumptions and result interpretation are morphing even though use of E.C. models has now been around for years.

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: Producing a crystal-clear balance roll-forward on time, obtaining a fresh model output the first time or providing model results for your business partners with a tight turnaround all depend on one thing: how fast the model engine runs. Authors explored various reasons behind significant computational power consumption, and discussed different ways to speed the computational process such as in-force population compression, model use case consolidation, code simplification and streamlining, and infrastructure automation, etc.

Description: In December 2007, Goldman Sachs launched a product called QxX index swap, which is designed to allow market participants to hedge or gain exposure to longevity and mortality risks. This presentation offers a quantitative analysis of this brand new financial innovation. First of all, the presentation sets up a risk-neutral framework to price QxX index swaps. This framework, which is based on the dynamics of death rates under a two-factor stochastic mortality model in a risk-adjusted probability measure, yields prices [spreads] that are fairly close to the spreads that Goldman Sachs currently offers. The presentation then explores the uncertainty involved in this model-based pricing framework. Specifically, it studies parameter risk by using Markov Chain Monte Carlo [MCMC] and model risk by examining structural changes in mortality dynamics. The results indicate that both model risk and parameter risk are significant. Actuaries should therefore be aware of these issues when placing a value on a longevity index swap.

Description: This presentation considers the pricing of European derivatives in a Black-Scholes model with stochastic volatility. The presentation shows how Parseval’s theorem may be used to express those prices as Fourier integrals. This is a significant improvement over Monte Carlo simulation in many cases. The main ingredient in this presentation's method is the Laplace transform of the ordinary [constant volatility] price of a put or call in the Black-Scholes model, where the transform is taken with respect to maturity [T]. The presentation derives these formulas and then applies them to the case where volatility is modelled as a Markov chain in continuous time, the so-called 'Markov regime switching model'. This model has been used previously in stochastic volatility modelling, but mostly with only N=2 states. The presentation shows how to use N=3 states without difficulty, and how larger number of states can be handled. Numerical illustrations are given, including the volatility smile in a three-state model.