Description: Logistic-type models for the force of mortality like those introduced by Perks or Kannisto provide better fit to mortality data of people aged over 85 than Makeham’s model where the force of mortality increases exponentially with age. However, the difficulty in estimating their parameters by the maximum likelihood method makes their use less popular among actuaries. For Kannisto’s model, this paper proposes a weighted least-squares estimator which can easily be calculated with any regression software. The estimator is shown to be consistent, asymptotically unbiased and normally distributed. For Perks’ model, using a Taylor’s series expansion, the estimation problem is again reduced to a least-squares problem. The various estimators proposed in the paper are compared numerically using Canadian mortality data.

Description: In this paper we compute the conditional and unconditional probability of ruin for an individual who wishes to consume a fixed periodic amount from an initial endowment invested in a portfolio earning a stochastic rate of return. From Retirement Needs Framework, M-RS00-1.

Description: 2011 SOA Enterprise Risk Management Symposium, Chicago. In this paper, a multivariate quasi-negative binomial distribution is proposed to model frequency dependence among different risk types. The operational risk diversification effect is illustrated through frequency dependency modeled by the bivariate quasi-negative binomial distribution under a framework of Monte Carlo simulation.

Description: This paper evaluates the current practice of operational risk management in the insurance sector. Operational risk is nothing new in insurance, but, because of regulatory requirements, companies have initiated computation of risk capital for their operational losses. The current effort to manage operational risk is not a naturally evolving phenomenon, and operational risk, in the Basel Committee on Banking Supervision’s Basel II definition, is unlikely to be a significant cause of insurers’ failure. In addition, the current Basel II definition of operational risk is not suitable for the insurance sector. Consequently, the invention of models and tools based on the definition is incomplete and illusionary. My findings are based on the analysis of dozens of interviews with insurance industry professionals. I demonstrate the way operational risk is quantified in practice, show that the result obtained from this computation is of littl e use in managerial decision making and propose a set of policy recommendations illustrating the characteristics of operational risk in insurance. This study can be used as a platform for launching dialogues to initiate fresh thinking about operational risk in insurance beyond the current artificial and narrow boundaries.

Description: This paper shows that the Esscher transform is also an efficient technique for valuing derivative securities if the logarithms of the prices of the primitive securities are governed by certain stochastic processes with stationary and independent increments. Two applications are presented, the first for valuing a European call option and the second for pricing derivative securities of multiple risky assets.

Description: This paper reviews validation for the model of a life insurance company's liabilities with actual company data. Two methods are reviewed: static and dynamic validation. From Society of Actuaries Financial Reporting Monograph, M-AS99-1.

Description: The purpose of this paper is to help practitioners and regulators more accurately quantify the potential impact of market risk on insurance products with equity-linked guarantees. To this end, this paper examines time series model selection and assessment based on residuals, with a focus on regime switching models. Also it discusses the difficulties in defining residuals for such processes and propose several possible alternatives. We determine that a stochastic approach to defining the residuals is the only way to generate residuals that are normally distributed under the model hypothesis.

Description: This paper focuses on business risks rather than market, credit and operational risks. The author proposes a bottom-up approach for modelling and measuring business risk where the dynamic of the underlying earnings is described in a continuous-time model.

Description: In this paper, a general multivariate duration analysis is introduced that does not depend on a mathematical formulation of the way in which a yield curve moves. To motivate the multivariate approach, simple examples are presented that demonstrate the limitations of the traditional model when yield curve shifts are not parallel.