A Dynamic Solvency Approach for Life Insurance

The paper investigates risk management processes in life insurance, in a perspective consistent with the framework of Solvency II. The paper starts with the breakdown of the business dynamics. This analysis provides for a complete depiction of risk and value driver within life business. The corresponding map is then put into the solvability context, in order to formally identify the equilibrium conditions. Considerations about the technical equilibrium of an insurance portfolio and the financial regulation lead to a dynamic system of solvency assessment. The formal model is applied to a life annuity cohort in a stochastic context in order to exemplify the potential of the model, especially referred to the need to frame solvency assessment in a dynamic perspective.Life insurance, financial risk, insolvency risk, capital adequacy, financial regulation

The current value of the mathematical provision: a financial risk prospect

The paper addresses the question of the calculation of the current value of the mathematical provision and moulds it in a deterministic and stochastic scenario, using a proper term structure of interest rates estimated by means of a Cox-Ingersoll-Ross model. It provides a complete and original year-by-year evaluation model for the business performance, and a closed solution for the current evaluation of the reserve, together with a comprehensive insight into the dynamics of the reserve connected to the selection of a defined term structure of interest rates. Moreover, the calculation of the VaR of the mathematical provision is prospected as risk measure useful to appreciate also the evaluation rate risk. Future research prospects concern the selection of the stochastic process used to describe the dynamics of the interest rates and the possible managerial and regulatory application of a VaR measure. The modelling has been applied, as an exemplification, to a life annuity portfolio but it can be easily replicated for any kind of policy and any kind of portfolios even non homogeneous.Risk indicators, life insurance, solvency, financial risk, demographic risk

Solvency of Life Insurance Companies: Methodological Issues

The paper deals with solvency assessment for life insurance business; some methodological issues concerning the solvency of life insurance companies, particularly connected to the investment risk, are suggested. Considerations about the technical equilibrium of an insurance portfolio and the financial regulation lead to a dynamic system involving risk measure and solvency assessment. The formal model is applied to a life annuity cohort in a stochastic context in order to exemplify the potential of the model, especially referred to the need to frame solvency assessment in a dynamic perspective

The uncertainty risk driver within a life annuity context: an overview

The paper analyzes the longevity effects on the portfolio valuations. This is a re levant topic, in particular from the perspective of insurers/sponsors of pension funds. The models chosen for actuarial calculations have to capture the survival trend and to pr oject its forecasted future impr ovements. The uncertainty in the choice is a huge concern and constitutes a relevant systematic risk driver itself, called unc ertainty risk therein. Aim of the paper is to measure the uncertainty risk and to show its trend in severa l contexts, meaningful in portfolio valuations. To this purpose the authors provide a suitable risk index and apply it in three different valuations: the initial value of an immediate life annuity portfolio; the fund of a pension annuity portfolio; the surplus of a portfolio consisting of deferred life annuities. Some graphs illustrate the results

Risk Sources in a Life Annuity Portfolio: Decomposition and Measurement Tools

The paper considers a model for a homogeneous portfolio of whole life annuities immediate. The aim is to study two risk factors: the investment risk and the insurance risk. A stochastic model of the rate of return is used to study these risk factors. Measures of the insurance risk and the investment risk for the entire portfolio are suggested. The problem of the longevity risk is presented, and its consequences with different projections of the mortality tables are analyzed. The model is applied to some concrete cases, and several illustrations show the importance of the two components of the riskiness in terms of the number of policies in the portfolio. Understanding these risks will allow insurance companies to control, to some extent, the overall risk of their annuity portfolios

Further Remarks on Risk Sources Measuring: The Case of a Life Annuity Portfolio

The paper considers a model that allows the actuary to measure the riskiness connected to the randomness of projected mortality tables in evaluating a portfolio of life annuities, obtaining a measure to reflect the risk associated with the randomness of the projection. The coherence of the risk parameters with the specific nature of the considered risk sources is also discussed. Numerical examples illustrate the results, showing the importance of the risk components in terms of the number of policies and comparing measure tools obtained by means of two procedures

Further Remarks on Risk Sources Measuring: The Case of a Life Annuity Portfolio

The paper considers a model that allows the actuary to measure the riskiness connected to the randomness of projected mortality tables in evaluating a portfolio of life annuities, obtaining a measure to reflect the risk associated with the randomness of the projection. The coherence of the risk parameters with the specific nature of the considered risk sources is also discussed. Numerical examples illustrate the results, showing the importance of the risk components in terms of the number of policies and comparing measure tools obtained by means of two procedures

A Sequential Monte Carlo Approach for the pricing of barrier option in a Stochastic Volatility Model

In this paper we propose a numerical scheme to estimate the price of a barrier option in a general framework. More precisely, we extend a classical Sequential Monte Carlo approach, developed under the hypothesis of deterministic volatility, to Stochastic Volatility models, in order to improve the efficiency of Standard Monte Carlo techniques in the case of barrier options whose underlying approaches the barriers. The paper concludes with the application of our procedure to two case studies in a SABR model

Lee–Carter model: assessing the potential to capture gender-related mortality dynamics

We investigate the ability of the Lee–Carter model to effectively estimate the gender gap ratio (GGR), the ratio between themale death rates over the female ones, by using a Cox–Ingersoll–Ross (CIR) process to provide a stochastic representation of the fitting errors. The novelty consists in the fact that we use the parameters characterizing the CIR process itself (long-term mean and volatility), in their intrinsic meanings, as quantitative measures of the long-term fitting attitude of the Lee–Carter model and synthetic indicators of the overall risk of this model. The analysis encompasses 25 European countries, to provide evidence-based indications about the goodness of fit of the Lee–Carter model in describing the GGR evolution.We highlight some stylized facts, namely systematic evidence about the fitting bias and the risk of the model across ages and countries. Furthermore, we perform a functional cluster analysis, allowing to capture similarities in the fitting performance of the Lee–Carter model among countries

The uncertainty risk driver within a life annuity context: an overview

The paper analyzes the longevity effects on the portfolio valuations. This is a relevant topic, in particular from the perspective of insurers/sponsors of pension funds. The models chosen for actuarial calculations have to capture the survival trend and to project its forecasted future improvements. The uncertainty in the choice is a huge concern and constitutes a relevant systematic risk driver itself, called uncertainty risk therein. Aim of the paper is to measure the uncertainty risk and to show its trend in several contexts, meaningful in portfolio valuations. To this purpose the authors provide a suitable risk index and apply it in three different valuations: the initial value of an immediate life annuity portfolio; the fund of a pension annuity portfolio; the surplus of a portfolio consisting of deferred life annuities. Some graphs illustrate the results