## 2014 |

Coppola, Mariarosaria; D’Amato, Valeria Further Results about Calibration of Longevity Risk for the Insurance Business (Journal Article) Applied Mathematics, 5 (4), 2014. (Abstract | Links | BibTeX | Tags: Expected Shortfall, Longevity Risk, Longevity Shocks, Solvency Capital Requirement, Solvency II) @article{Coppola2014, title = {Further Results about Calibration of Longevity Risk for the Insurance Business}, author = {Mariarosaria Coppola and Valeria D’Amato}, url = {http://file.scirp.org/Html/7-7401864_43570.htm}, doi = {DOI:10.4236/am.2014.54061}, year = {2014}, date = {2014-03-10}, journal = {Applied Mathematics}, volume = {5}, number = {4}, publisher = {Scientific Research Publishing}, abstract = {In life insurance business, longevity risk, i.e. the risk that the insured population lives longer than the expected, represents the heart of the risk assessment, having significant impact in terms of solvency capital requirements (SCRs) needed to front the firm obligations. The credit crisis has shown that systemic risk as longevity risk is relevant and that for many insurers it is actually the dominant risk. With the adoption of the Solvency II directive, a new area for insurance in terms of solvency regulation has been opened up. The international guidelines prescribe a market consistent valuation of balance sheets, where the solvency capital requirements to be set aside are calculated according to a modular structure. By mapping the main risk affecting the insurance portfolio, the capital amount able to cover the liabilities corresponds to each measured risk. In Solvency II, the longevity risk is included into underwriting risk module. In particular, the rules propose that companies use a standard model for measuring the SCRs. Nevertheless, the legislation under consideration allows designing tailor-made internal models. As regards the longevity risk assessment, the regulatory standard model leads to noteworthy inconsistencies. In this paper, we propose a stochastic volatility model combined with a so-called coherent risk measure as the expected shortfall for measuring the SCRs according to more realistic assumptions on future evolution of longevity trend. Finally empirical evidence is provided.}, keywords = {Expected Shortfall, Longevity Risk, Longevity Shocks, Solvency Capital Requirement, Solvency II}, pubstate = {published}, tppubtype = {article} } In life insurance business, longevity risk, i.e. the risk that the insured population lives longer than the expected, represents the heart of the risk assessment, having significant impact in terms of solvency capital requirements (SCRs) needed to front the firm obligations. The credit crisis has shown that systemic risk as longevity risk is relevant and that for many insurers it is actually the dominant risk. With the adoption of the Solvency II directive, a new area for insurance in terms of solvency regulation has been opened up. The international guidelines prescribe a market consistent valuation of balance sheets, where the solvency capital requirements to be set aside are calculated according to a modular structure. By mapping the main risk affecting the insurance portfolio, the capital amount able to cover the liabilities corresponds to each measured risk. In Solvency II, the longevity risk is included into underwriting risk module. In particular, the rules propose that companies use a standard model for measuring the SCRs. Nevertheless, the legislation under consideration allows designing tailor-made internal models. As regards the longevity risk assessment, the regulatory standard model leads to noteworthy inconsistencies. In this paper, we propose a stochastic volatility model combined with a so-called coherent risk measure as the expected shortfall for measuring the SCRs according to more realistic assumptions on future evolution of longevity trend. Finally empirical evidence is provided. |

Coppola, Mariarosaria; D’Amato, Valeria Basis risk in Solvency Capital Requirements for longevity risk (Journal Article) Investment Management and Financial Innovations, 11 (3), pp. 53-57, 2014. (Abstract | Links | BibTeX | Tags: Basis risk, Longevity Risk, net asset value, Solvency Capital Requirement) @article{Coppola2014a, title = {Basis risk in Solvency Capital Requirements for longevity risk}, author = {Mariarosaria Coppola and Valeria D’Amato}, url = {http://www.labstat.it/home/wp-content/uploads/2016/04/imfi_en_2014_03_Coppola.pdf}, year = {2014}, date = {2014-01-01}, journal = {Investment Management and Financial Innovations}, volume = {11}, number = {3}, pages = {53-57}, abstract = {The international guidelines of Solvency II prescribe a regulation which should help insurance industry mitigating undesired outcomes arising from the exposure to the systemic risks. In particular, the rules on Solvency Capital Requirements recommend to separately compute them for each risk factor, where for the longevity risk sub-module the Solvency Capital Requirement results by the change in net asset value (NAV) due to a longevity shock which actually assumes a permanent reduction of the mortality rates for all ages by 20%. Nevertheless, the data based on statistics coming from various national longevity indices differ from those deriving from the regulatory assessment of solvency, determining significant underestimations or overestimations: a basis risk comes from a questionable adequacy of the longevity shock. This paper contributes to the discussion on Solvency Capital Requirements by focusing on the main features of the potential basis risk which determines the inappropriate capitalization of insurance companies. Furthermore we analyze the sensitivities of the basis risk to different ages for better assessing the actual risk of insurance portfolios. }, keywords = {Basis risk, Longevity Risk, net asset value, Solvency Capital Requirement}, pubstate = {published}, tppubtype = {article} } The international guidelines of Solvency II prescribe a regulation which should help insurance industry mitigating undesired outcomes arising from the exposure to the systemic risks. In particular, the rules on Solvency Capital Requirements recommend to separately compute them for each risk factor, where for the longevity risk sub-module the Solvency Capital Requirement results by the change in net asset value (NAV) due to a longevity shock which actually assumes a permanent reduction of the mortality rates for all ages by 20%. Nevertheless, the data based on statistics coming from various national longevity indices differ from those deriving from the regulatory assessment of solvency, determining significant underestimations or overestimations: a basis risk comes from a questionable adequacy of the longevity shock. This paper contributes to the discussion on Solvency Capital Requirements by focusing on the main features of the potential basis risk which determines the inappropriate capitalization of insurance companies. Furthermore we analyze the sensitivities of the basis risk to different ages for better assessing the actual risk of insurance portfolios. |

Coppola, Mariarosaria; D’Amato, Valeria The Solvency Capital Requirement Management for an Insurance Company (Book Chapter) Perna, Cira; Sibillo, Marilena (Ed.): Mathematical and Statistical Methods for Actuarial Sciences and Finance, pp. 65-68, Springer International Publishing, 2014, ISBN: 978-3-319-05013-3. (Abstract | Links | BibTeX | Tags: Expected Shortfall, Longevity Risk, Longevity Shocks, Solvency Capital Requirement) @inbook{Coppola2014b, title = {The Solvency Capital Requirement Management for an Insurance Company}, author = {Mariarosaria Coppola and Valeria D’Amato}, editor = {Cira Perna and Marilena Sibillo}, url = {http://link.springer.com/chapter/10.1007/978-3-319-05014-0_15}, doi = {10.1007/978-3-319-05014-0_15}, isbn = {978-3-319-05013-3}, year = {2014}, date = {2014-01-01}, booktitle = {Mathematical and Statistical Methods for Actuarial Sciences and Finance}, pages = {65-68}, publisher = {Springer International Publishing}, abstract = {Longevity risk plays a central role in the insurance company management since only careful assumptions about future evolution of mortality phenomenon allows the company to correctly front its future obligations. According to Solvency II longevity risk represents a sub-module of the underwriting risk module in the regulatory standard formula. In this paper we examine the adequacy of the shock’s structure suggested by the standard formula studying its impact on the solvency capital requirements and liabilities at different ages. In particular, we propose an alternative to the regulatory standard model represented by a flexible internal model. The innovative approach hinges on a stochastic volatility model and a so-called coherent risk measure as the expected shortfall. An empirical analysis is provided.}, keywords = {Expected Shortfall, Longevity Risk, Longevity Shocks, Solvency Capital Requirement}, pubstate = {published}, tppubtype = {inbook} } Longevity risk plays a central role in the insurance company management since only careful assumptions about future evolution of mortality phenomenon allows the company to correctly front its future obligations. According to Solvency II longevity risk represents a sub-module of the underwriting risk module in the regulatory standard formula. In this paper we examine the adequacy of the shock’s structure suggested by the standard formula studying its impact on the solvency capital requirements and liabilities at different ages. In particular, we propose an alternative to the regulatory standard model represented by a flexible internal model. The innovative approach hinges on a stochastic volatility model and a so-called coherent risk measure as the expected shortfall. An empirical analysis is provided. |

## 2013 |

Coppola, Mariarosaria; D’Amato, Valeria; Levantesi, Susanna; Menzietti, Massimiliano; Russolillo, Maria Longevity risk hedging and basis risk (Proceeding) 2013. (Abstract | BibTeX | Tags: Basis risk, FDM, functional demographic model, Longevity Risk) @proceedings{Coppola2013, title = {Longevity risk hedging and basis risk}, author = {Mariarosaria Coppola and Valeria D’Amato and Susanna Levantesi and Massimiliano Menzietti and Maria Russolillo}, year = {2013}, date = {2013-07-03}, booktitle = {The 17th International Congress on Insurance: Mathematics and Economics, Copenhagen, July 1-3, 2013}, pages = {40-41}, abstract = {The improvements of longevity are intensifying the need for capital markets to be used to manage and transfer the risk through longevity-linked securities. Nevertheless the difference between the reference population of the hedging instrument ("hedging population") and the population of members of a pension plan or the beneficiaries of an annuity portfolio ("exposed population") determines a signicant heterogeneity which causes the so-called basis risk. The paper focuses on the longevity risk management by securitization, providing a framework for measuring the basis risk impact on the hedging strategies. To this aim we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting.In order to quantify the basis risk, we define a stochastic mortality model for two populations based on the FDM framework. We consider both an independent FDM (the hedging population is independent from the exposed population) and a joint FDM (both populations are jointly driven by a single index of mortality over time). Under the proposed mortality model, we build a longevity hedging strategy involving a portfolio of q-forwards calibrated through the key-q-duration (KQD), i.e. the annuity portfolios price sensitivity to a shift in a key mortality rate . The shifts are adjusted with the standard deviation of the exposed population mortality in order to realise a more effective hedge. In order to analyse the hedge effectiveness we consider the present value of both unexpected cash flows of the insurance portfolio and payoffs from the q-forwards involved in the hedging portfolio. The KQD of these quantities as well as an adjustment factor depending on the specified mortality model allow to find the required notional amount of the q-forwards in presence of basis risk.}, keywords = {Basis risk, FDM, functional demographic model, Longevity Risk}, pubstate = {published}, tppubtype = {proceedings} } The improvements of longevity are intensifying the need for capital markets to be used to manage and transfer the risk through longevity-linked securities. Nevertheless the difference between the reference population of the hedging instrument ("hedging population") and the population of members of a pension plan or the beneficiaries of an annuity portfolio ("exposed population") determines a signicant heterogeneity which causes the so-called basis risk. The paper focuses on the longevity risk management by securitization, providing a framework for measuring the basis risk impact on the hedging strategies. To this aim we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting.In order to quantify the basis risk, we define a stochastic mortality model for two populations based on the FDM framework. We consider both an independent FDM (the hedging population is independent from the exposed population) and a joint FDM (both populations are jointly driven by a single index of mortality over time). Under the proposed mortality model, we build a longevity hedging strategy involving a portfolio of q-forwards calibrated through the key-q-duration (KQD), i.e. the annuity portfolios price sensitivity to a shift in a key mortality rate . The shifts are adjusted with the standard deviation of the exposed population mortality in order to realise a more effective hedge. In order to analyse the hedge effectiveness we consider the present value of both unexpected cash flows of the insurance portfolio and payoffs from the q-forwards involved in the hedging portfolio. The KQD of these quantities as well as an adjustment factor depending on the specified mortality model allow to find the required notional amount of the q-forwards in presence of basis risk. |

Coppola, Mariarosaria; D’Amato, Valeria The SCR adequacy according to the volatility longevity shocks (Proceeding) ISAST: International Society for the Advancement of Science and Technology. 1st ed, 2013. (Abstract | BibTeX | Tags: Longevity Risk, SCRLong, Solvency II) @proceedings{Coppola2013a, title = {The SCR adequacy according to the volatility longevity shocks}, author = {Mariarosaria Coppola and Valeria D’Amato}, editor = {Christos H. Skiadas}, year = {2013}, date = {2013-06-28}, booktitle = {Book of Abstracts 15th Applied Stochastic Models and Data Analysis International Conference, ASMDA, Matarò-Spain,, 25-28 June 2013}, pages = {56}, publisher = {ISAST: International Society for the Advancement of Science and Technology. 1st ed}, abstract = {The improvements in longevity observed in many countries over the past century have been significant. The risk that the longevity experience is higher than the one forecasted, i.e. longevity risk, is explicitly consideredin Solvency II standard formula as a sub-module of the life underwriting risk module. The life underwriting risk module includes all the life insurance and reinsurance obligations, except the SLT health insurance obligations (EIOPA 2012), where the longevity risk is one of the seven sub-modules. According to Solvency II, solvency capital requirements (from herein SCRs) can be computed by a standard formula or an internal model. Nevertheless, the scenario in which the insurance companies operate is often more complex than that one assumed by the standard formula. According to the standard formula the SCR is represented as the change in net asset value due to longevity shock which is a permanent 20% reduction of mortality rates for all ages. A constant shock is not reasonable for all ages and maturities. The scenario related to the standard formula may lead to a biased allocation of capital, because of the volatility of longevity phenomenon in respect of different ages. In this paper we examine the adequacy of SCRs on the basis of the standard formula. To correctly calculate the solvency capital requirement we follow a multi-period approach in the sense that we evaluate at the beginning of each year the amount of capital that the insurer need to meet its future obligations year by year till the contract will be in force. We examine the adequacy of the shocks structure suggested by the standard formula studying its impact on the SCR for longevity risk (SCRLong) and liabilities at different ages.}, keywords = {Longevity Risk, SCRLong, Solvency II}, pubstate = {published}, tppubtype = {proceedings} } The improvements in longevity observed in many countries over the past century have been significant. The risk that the longevity experience is higher than the one forecasted, i.e. longevity risk, is explicitly consideredin Solvency II standard formula as a sub-module of the life underwriting risk module. The life underwriting risk module includes all the life insurance and reinsurance obligations, except the SLT health insurance obligations (EIOPA 2012), where the longevity risk is one of the seven sub-modules. According to Solvency II, solvency capital requirements (from herein SCRs) can be computed by a standard formula or an internal model. Nevertheless, the scenario in which the insurance companies operate is often more complex than that one assumed by the standard formula. According to the standard formula the SCR is represented as the change in net asset value due to longevity shock which is a permanent 20% reduction of mortality rates for all ages. A constant shock is not reasonable for all ages and maturities. The scenario related to the standard formula may lead to a biased allocation of capital, because of the volatility of longevity phenomenon in respect of different ages. In this paper we examine the adequacy of SCRs on the basis of the standard formula. To correctly calculate the solvency capital requirement we follow a multi-period approach in the sense that we evaluate at the beginning of each year the amount of capital that the insurer need to meet its future obligations year by year till the contract will be in force. We examine the adequacy of the shocks structure suggested by the standard formula studying its impact on the SCR for longevity risk (SCRLong) and liabilities at different ages. |

## 2012 |

Coppola, Mariarosaria; D’Amato, Valeria; Levantesi, Susanna; Menzietti, Massimiliano; Russolillo, Maria Managing basis risk in longevity hedging strategies (Proceeding) 2012. (Abstract | BibTeX | Tags: Basis risk, FDM, Longevity Risk) @proceedings{Coppola2012b, title = {Managing basis risk in longevity hedging strategies}, author = {Mariarosaria Coppola and Valeria D’Amato and Susanna Levantesi and Massimiliano Menzietti and Maria Russolillo}, year = {2012}, date = {2012-09-07}, booktitle = {1st European Actuarial Journal Conference. University of Lausanne and Swiss Association of Actuaries, 6-7 September 2012}, pages = {79-80}, abstract = {In the last years significant tools have been developed for transferring longevity risk to the capital markets, bringing additional capacity, flexibility and transparency to complement existing insurance solutions. Specifically, hedging longevity risk with index-based longevity hedges can have several advantages but the difference between the insurer’s mortality experience based on annuitant mortality and the hedged standardized index based on reference population mortality gives rise to the so-called basis risk. The presence of basis risk means that hedge effectiveness will not be perfect and that, post implementation, the hedged position will still have some residual risk. The present paper seeks to contribute to that literature by setting out a framework for quantifying the basis risk. In particular we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting. The literature suggests that the FDM forecast accuracy is arguably connected to the model structure, combining functional data analysis, nonparametric smoothing and robust statistics. In particular, the decomposition of the fitted curve via basis functions represents the advantage, since they capture the variability of the mortality trend, by separating out the effects of several orthogonal components. Specifically, while most existing models are designed for a single population the research objective is to model mortality of two populations as in Li and Hardy (2011) in order to align with the hedging purpose. Under the proposed mortality model, we develop an optimal longevity hedging strategy involving mortality linked securities and following the immunization theory approach. We firstly assume no difference between the two population mortalities (no basis risk) and we show as such a strategy could be not perfectly effective when difference in the reference population respect to mortality index’ one emerges and basis risk is measured. Afterwards an optimal hedging strategies is developed explicitly including basis risk. We show as the longevity hedging could be more effective although still not perfect.}, keywords = {Basis risk, FDM, Longevity Risk}, pubstate = {published}, tppubtype = {proceedings} } In the last years significant tools have been developed for transferring longevity risk to the capital markets, bringing additional capacity, flexibility and transparency to complement existing insurance solutions. Specifically, hedging longevity risk with index-based longevity hedges can have several advantages but the difference between the insurer’s mortality experience based on annuitant mortality and the hedged standardized index based on reference population mortality gives rise to the so-called basis risk. The presence of basis risk means that hedge effectiveness will not be perfect and that, post implementation, the hedged position will still have some residual risk. The present paper seeks to contribute to that literature by setting out a framework for quantifying the basis risk. In particular we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting. The literature suggests that the FDM forecast accuracy is arguably connected to the model structure, combining functional data analysis, nonparametric smoothing and robust statistics. In particular, the decomposition of the fitted curve via basis functions represents the advantage, since they capture the variability of the mortality trend, by separating out the effects of several orthogonal components. Specifically, while most existing models are designed for a single population the research objective is to model mortality of two populations as in Li and Hardy (2011) in order to align with the hedging purpose. Under the proposed mortality model, we develop an optimal longevity hedging strategy involving mortality linked securities and following the immunization theory approach. We firstly assume no difference between the two population mortalities (no basis risk) and we show as such a strategy could be not perfectly effective when difference in the reference population respect to mortality index’ one emerges and basis risk is measured. Afterwards an optimal hedging strategies is developed explicitly including basis risk. We show as the longevity hedging could be more effective although still not perfect. |

Coppola, Mariarosaria; D’Amato, Valeria Backtesting the solvency capital requirement for longevity risk (Journal Article) The Journal of Risk Finance, 13 (4), pp. 309-319, 2012, ISSN: 1526-5943. (Abstract | Links | BibTeX | Tags: Backtest, Capital, Finance, Insurance companies, Iterative Lee Carter model, Life annuity portfolio, Life insurance, Longevity Risk, Regulation, Risk analysis, Solvency Capital Requirement, Solvency II) @article{Coppola2012b, title = {Backtesting the solvency capital requirement for longevity risk}, author = {Mariarosaria Coppola and Valeria D’Amato}, url = {http://www.emeraldinsight.com/doi/abs/10.1108/15265941211254444}, doi = {http://dx.doi.org/10.1108/15265941211254444}, issn = {1526-5943}, year = {2012}, date = {2012-08-10}, journal = {The Journal of Risk Finance}, volume = {13}, number = {4}, pages = {309-319}, publisher = {Emerald Group Publishing Limited}, abstract = {The determination of the capital requirements represents the first Pillar of Solvency II. The main purpose of the new solvency regulation is to obtain more realistic modelling and assessment of the different risks insurance companies are exposed to in a balance‐sheet perspective. In this context, the Solvency Capital Requirement (SCR) standard calculation is based on a modular approach, where the overall risk is split into several modules and submodules. In Solvency II, standard formula longevity risk is explicitly considered. The purpose of this paper is to look at the backtesting approach for measuring the consistency of SCR calculations for life insurance policies.}, keywords = {Backtest, Capital, Finance, Insurance companies, Iterative Lee Carter model, Life annuity portfolio, Life insurance, Longevity Risk, Regulation, Risk analysis, Solvency Capital Requirement, Solvency II}, pubstate = {published}, tppubtype = {article} } The determination of the capital requirements represents the first Pillar of Solvency II. The main purpose of the new solvency regulation is to obtain more realistic modelling and assessment of the different risks insurance companies are exposed to in a balance‐sheet perspective. In this context, the Solvency Capital Requirement (SCR) standard calculation is based on a modular approach, where the overall risk is split into several modules and submodules. In Solvency II, standard formula longevity risk is explicitly considered. The purpose of this paper is to look at the backtesting approach for measuring the consistency of SCR calculations for life insurance policies. |

## 2011 |

Coppola, Mariarosaria; Lorenzo, Emilia Di; Orlando, Albina; Politano, Massimiliano Longevity risk: a stochastic dynamic approach (Proceeding) 2011. (Abstract | BibTeX | Tags: CIR model, Longevity Risk, stochastic methods) @proceedings{Coppola2011e, title = {Longevity risk: a stochastic dynamic approach}, author = {Mariarosaria Coppola and Emilia Di Lorenzo and Albina Orlando and Massimiliano Politano}, year = {2011}, date = {2011-06-10}, booktitle = {XIV ASMDA Conference, Rome, Italy, 7-10 June 2011}, abstract = {The paper focuses on the study of hazard mortality rates evolution in time to front the actuarial issue of longevity risk. Whatever hypothesis about future mortality, a correct evaluation of the expected mortality randomness requires the use of a suitable stochastic model. In this context, we first propose a computational tractable approach based on a CIR type stochastic process for modeling the future mortality rates. Then we investigate the impact of adverse effects on the mortality dynamics by a quantile analysis. Numerical applications to the Italian population are discussed.}, keywords = {CIR model, Longevity Risk, stochastic methods}, pubstate = {published}, tppubtype = {proceedings} } The paper focuses on the study of hazard mortality rates evolution in time to front the actuarial issue of longevity risk. Whatever hypothesis about future mortality, a correct evaluation of the expected mortality randomness requires the use of a suitable stochastic model. In this context, we first propose a computational tractable approach based on a CIR type stochastic process for modeling the future mortality rates. Then we investigate the impact of adverse effects on the mortality dynamics by a quantile analysis. Numerical applications to the Italian population are discussed. |

Coppola, Mariarosaria; Lorenzo, Emilia Di; Orlando, Albina; Marilena Sibillo, Solvency analysis and demographic risk measures (Journal Article) The Journal of Risk Finance, 12 (3), pp. 252 - 269, 2011, ISSN: 1526-5943. (Abstract | Links | BibTeX | Tags: Financial risk, Insurance, Longevity Risk, Model risk, Quantile surplus, Risk index, Ruin probability, Stochastic surplus) @article{Coppola2011, title = {Solvency analysis and demographic risk measures}, author = {Mariarosaria Coppola and Emilia Di Lorenzo and Albina Orlando and Marilena Sibillo,}, url = {http://www.emeraldinsight.com/doi/abs/10.1108/15265941111158451}, doi = {http://dx.doi.org/10.1108/15265941111158451}, issn = {1526-5943}, year = {2011}, date = {2011-01-01}, journal = {The Journal of Risk Finance}, volume = {12}, number = {3}, pages = {252 - 269}, abstract = {The demographic risk is the risk due to the uncertainty in the demographic scenario assumptions by which life insurance products are designed and valued. The uncertainty lies both in the accidental (insurance risk) and systematic (longevity risk) deviations of the number of deaths from the value anticipated for it. This last component gives rise to the risk due to the randomness in the choice of the survival model for valuations (model risk or projection risk). If the insurance risk component can be assumed negligible for well‐diversified portfolios, as in the case of pension annuities, longevity risk is crucial in the actuarial valuations. The question is particularly decisive in contexts in which the longevity phenomenon of the population is strong and pension annuity portfolios constitute a meaningful slice of the financial market – both typical elements of Western economies. The paper aims to focus on the solvency appraisal for a portfolio of life annuities, deepening the impact of the demographic risk according to suitable risk indexes apt to describe its evolution in time.}, keywords = {Financial risk, Insurance, Longevity Risk, Model risk, Quantile surplus, Risk index, Ruin probability, Stochastic surplus}, pubstate = {published}, tppubtype = {article} } The demographic risk is the risk due to the uncertainty in the demographic scenario assumptions by which life insurance products are designed and valued. The uncertainty lies both in the accidental (insurance risk) and systematic (longevity risk) deviations of the number of deaths from the value anticipated for it. This last component gives rise to the risk due to the randomness in the choice of the survival model for valuations (model risk or projection risk). If the insurance risk component can be assumed negligible for well‐diversified portfolios, as in the case of pension annuities, longevity risk is crucial in the actuarial valuations. The question is particularly decisive in contexts in which the longevity phenomenon of the population is strong and pension annuity portfolios constitute a meaningful slice of the financial market – both typical elements of Western economies. The paper aims to focus on the solvency appraisal for a portfolio of life annuities, deepening the impact of the demographic risk according to suitable risk indexes apt to describe its evolution in time. |

# Publications

## 2014 |

Further Results about Calibration of Longevity Risk for the Insurance Business (Journal Article) Applied Mathematics, 5 (4), 2014. |

Basis risk in Solvency Capital Requirements for longevity risk (Journal Article) Investment Management and Financial Innovations, 11 (3), pp. 53-57, 2014. |

The Solvency Capital Requirement Management for an Insurance Company (Book Chapter) Perna, Cira; Sibillo, Marilena (Ed.): Mathematical and Statistical Methods for Actuarial Sciences and Finance, pp. 65-68, Springer International Publishing, 2014, ISBN: 978-3-319-05013-3. |

## 2013 |

Longevity risk hedging and basis risk (Proceeding) 2013. |

The SCR adequacy according to the volatility longevity shocks (Proceeding) ISAST: International Society for the Advancement of Science and Technology. 1st ed, 2013. |

## 2012 |

Managing basis risk in longevity hedging strategies (Proceeding) 2012. |

Backtesting the solvency capital requirement for longevity risk (Journal Article) The Journal of Risk Finance, 13 (4), pp. 309-319, 2012, ISSN: 1526-5943. |

## 2011 |

Longevity risk: a stochastic dynamic approach (Proceeding) 2011. |

Solvency analysis and demographic risk measures (Journal Article) The Journal of Risk Finance, 12 (3), pp. 252 - 269, 2011, ISSN: 1526-5943. |