This thesis is a collection of four different contributions to the analysis, valuation and risk management of life insurance products and life insurance portfolios at future time horizons, as well as it examines the extent of longevity risk for future cohorts. To calculate the implied conditional expectations arising in these problems, we propose to apply a methodology based on regression and simulation methods. In particular, in the first paper, we deal with the valuation of future life annuity contracts by developing a methodology based on the Least-Squares Monte Carlo (LSMC) approach, i.e., by combining Monte Carlo simulation with Least-Squares regression to evaluate conditional expectations, a technique widely adopted for pricing American contingent claims, allowing to avoid the use of nested simulations. To test the accuracy and the efficiency of the proposed methodology, we perform an extensive comparative analysis by exploiting a benchmark based on a nested simulations procedure. We consider first a simplified computational framework where just one risk factor is taken into account and then we introduce multiple sources of risk. We aim at exploring the resulting algorithm and several of its variants to the valuation (more generally, to the study of the distribution) of annuity values at any future date when the model employed involves processes for interest rates and mortality that have no closed-form expressions for expected present values of pure endowments. The methodology has multiple applications, from the pricing of traditional, equity-indexed, variable annuities, guaranteed annuity options, pension buy-in/out and other pension risk management problems. In the second paper we focus on a demographic application of the LSMC method. Specifically, we aim at studying the time evolution of some longevity metric, such as future life expectancy and lifespan disparity. This study will be conducted by adopting a cohort based perspective in contrast to the usual practice based on period life tables. Indeed, as it will be discussed, the use of cohort life tables automatically implies conditional arguments which will be faced with the LSMC method. A comparative analysis between cohort and period valuations will be provided in order to assess their forecast difference. To project mortality onto the future, we exploit extrapolative procedures; in particular, we consider single and multi-population mortality models in order to take into account the inter-dependence in mortality evolution among sub-populations. Overall, this will provide a very flexible tool which can be used for any other longevity measure involving conditional expectations, where cohort based measurements are often replaced by period ones for computational simplicity. In the third paper, we present an R function which has been developed on the basis of the previously mentioned papers. The function will be part of the well known and widely used R package for stochastic mortality StMoMo, giving also the possibility to accommodate customized mortality forecasts and to include stochastic interest rate models. We illustrate some of the capabilities of the function and introduce the corresponding new R class on which it is possible to use many basic R methods. Finally, in the fourth paper, we address the problem of approximating the future value distribution of a large and heterogeneous life insurance portfolio which would play a relevant role, for instance, for solvency capital requirement valuations. This work is based on a metamodel by which we first select a subset of representative policies in the portfolio and then approximate the distribution of a single policy and of the entire portfolio by means of two different approaches, the ordinary least square, and a regression method based on the class of generalized beta distribution of the second kind. The reliability of the proposed methodology is investigated through extensive numerical experiments.

Some Life Insurance Applications of Regression and Simulation Methods / Fabio Viviano , 2022 Mar 03. 34. ciclo, Anno Accademico 2020/2021.

Some Life Insurance Applications of Regression and Simulation Methods

VIVIANO, FABIO
2022-03-03

Abstract

This thesis is a collection of four different contributions to the analysis, valuation and risk management of life insurance products and life insurance portfolios at future time horizons, as well as it examines the extent of longevity risk for future cohorts. To calculate the implied conditional expectations arising in these problems, we propose to apply a methodology based on regression and simulation methods. In particular, in the first paper, we deal with the valuation of future life annuity contracts by developing a methodology based on the Least-Squares Monte Carlo (LSMC) approach, i.e., by combining Monte Carlo simulation with Least-Squares regression to evaluate conditional expectations, a technique widely adopted for pricing American contingent claims, allowing to avoid the use of nested simulations. To test the accuracy and the efficiency of the proposed methodology, we perform an extensive comparative analysis by exploiting a benchmark based on a nested simulations procedure. We consider first a simplified computational framework where just one risk factor is taken into account and then we introduce multiple sources of risk. We aim at exploring the resulting algorithm and several of its variants to the valuation (more generally, to the study of the distribution) of annuity values at any future date when the model employed involves processes for interest rates and mortality that have no closed-form expressions for expected present values of pure endowments. The methodology has multiple applications, from the pricing of traditional, equity-indexed, variable annuities, guaranteed annuity options, pension buy-in/out and other pension risk management problems. In the second paper we focus on a demographic application of the LSMC method. Specifically, we aim at studying the time evolution of some longevity metric, such as future life expectancy and lifespan disparity. This study will be conducted by adopting a cohort based perspective in contrast to the usual practice based on period life tables. Indeed, as it will be discussed, the use of cohort life tables automatically implies conditional arguments which will be faced with the LSMC method. A comparative analysis between cohort and period valuations will be provided in order to assess their forecast difference. To project mortality onto the future, we exploit extrapolative procedures; in particular, we consider single and multi-population mortality models in order to take into account the inter-dependence in mortality evolution among sub-populations. Overall, this will provide a very flexible tool which can be used for any other longevity measure involving conditional expectations, where cohort based measurements are often replaced by period ones for computational simplicity. In the third paper, we present an R function which has been developed on the basis of the previously mentioned papers. The function will be part of the well known and widely used R package for stochastic mortality StMoMo, giving also the possibility to accommodate customized mortality forecasts and to include stochastic interest rate models. We illustrate some of the capabilities of the function and introduce the corresponding new R class on which it is possible to use many basic R methods. Finally, in the fourth paper, we address the problem of approximating the future value distribution of a large and heterogeneous life insurance portfolio which would play a relevant role, for instance, for solvency capital requirement valuations. This work is based on a metamodel by which we first select a subset of representative policies in the portfolio and then approximate the distribution of a single policy and of the entire portfolio by means of two different approaches, the ordinary least square, and a regression method based on the class of generalized beta distribution of the second kind. The reliability of the proposed methodology is investigated through extensive numerical experiments.
3-mar-2022
Some Life Insurance Applications of Regression and Simulation Methods / Fabio Viviano , 2022 Mar 03. 34. ciclo, Anno Accademico 2020/2021.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1224170
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