Portfolio Of Life Insurance Policies Research Articles

Shortcuts for the construction of sub-annual life tables

AbstractFuelled by the big data explosion, a new methodology to estimate sub-annual death probabilities has recently been proposed, opening new insurance business opportunities. This new approach exploits all the detailed information available from millions of microdata records to develop seasonal-ageing indexes (SAIs) from which sub-annual (quarterly) life tables can be derived from annual tables. In this paper, we explore whether a shortcut could be taken in the estimation of SAIs and (life insurance) sub-annual death rates. We propose three different approximations, in which estimates are attained by using just a small bunch of thousands of data records and assess their impact on several competitive markets defined from an actual portfolio of life insurance policies. Our analyses clearly point to the shortcuts as good practical alternatives that can be used in real-life insurance markets. Noticeably, we see that embracing the new quarterly based approach, even using only an approximation (shortcut), is economically preferable to using the associated annual table, offering a significant competitive advantage to the company adopting this innovation.

Global Optimization for Automatic Model Points Selection in Life Insurance Portfolios

Starting from an original portfolio of life insurance policies, in this article we propose a methodology to select model points portfolios that reproduce the original one, preserving its market risk under a certain measure. In order to achieve this goal, we first define an appropriate risk functional that measures the market risk associated to the interest rates evolution. Although other alternative interest rate models could be considered, we have chosen the LIBOR (London Interbank Offered Rate) market model. Once we have selected the proper risk functional, the problem of finding the model points of the replicating portfolio is formulated as a problem of minimizing the distance between the original and the target model points portfolios, under the measure given by the proposed risk functional. In this way, a high-dimensional global optimization problem arises and a suitable hybrid global optimization algorithm is proposed for the efficient solution of this problem. Some examples illustrate the performance of a parallel multi-CPU implementation for the evaluation of the risk functional, as well as the efficiency of the hybrid Basin Hopping optimization algorithm to obtain the model points portfolio.

Efficient Model Points Selection in Insurance by Parallel Global Optimization Using Multi CPU and Multi GPU

In the insurance sector, Asset Liability Management refers to the joint management of the assets and liabilities of a company. The liabilities mainly consist of the policies portfolios of the insurance company, which usually contain a large amount of policies. In the article, the authors mainly develop a highly efficient automatic generation of model points portfolios to represent much larger real policies portfolios. The obtained model points portfolio must retain the market risk properties of the initial portfolio. For this purpose, the authors propose a risk measure that incorporates the uncertain evolution of interest rates to the portfolios of life insurance policies, following Ferri (Optimal model points portfolio in life, 2019, arXiv:1808.00866). This problem can be formulated as a minimization problem that has to be solved using global numerical optimization algorithms. The cost functional measures an appropriate distance between the original and the model point portfolios. In order to solve this problem in a reasonable computing time, sequential implementations become prohibitive, so that the authors speed up the computations by developing a high performance computing framework that uses hybrid architectures, which consist of multi CPUs together with accelerators (multi GPUs). Thus, in graphic processor units (GPUs) the evaluation of the cost function is parallelized, which requires a Monte Carlo method. For the optimization problem, the authors compare a metaheuristic stochastic differential evolution algorithm with a multi path variant of hybrid global optimization Basin Hopping algorithms, which combines Simulated Annealing with gradient local searchers (Ferreiro et al. in Appl Math Comput 356:282–298, 2019a). Both global optimizers are parallelized in a multi CPU together with a multi GPU setting.

Biometric worst-case scenarios for multi-state life insurance policies

It is common actuarial practice to calculate premiums and reserves under a set of biometric assumptions that represent a worst-case scenario for the insurer. The new solvency regime of the European Union (Solvency II) also uses worst-case scenarios for the calculation of solvency capital requirements for life insurance business. Surprisingly, the actuarial literature so far offers no exact method for the construction of biometric scenarios that let premiums and reserves be always on the safe side with respect to a given confidence band for the biometric second-order basis. The present paper partly fills this gap by introducing a general method that allows one to construct such scenarios for homogenous portfolios of life insurance policies. The results are especially informative for life insurance policies with mixed character (e.g. survival and occurrence character). Two examples are given that illustrate the new method, demonstrate its usefulness for the calculation of premiums and reserves, and show how the new approach could improve the calculation of biometric solvency reserves for Solvency II.

On parallel asset-liability management in life insurance: a forward risk-neutral approach

In this paper we discuss the development of a valuation system of asset-liability management of portfolios of life insurance policies on advanced architectures. According to the new rules of the Solvency II project, numerical simulations must provide reliable estimates of the relevant quantities involved in the contracts; therefore, valuation processes have to rely on accurate algorithms able to provide solutions in a suitable turnaround time. Our target is to develop an effective valuation software. At this aim we first introduce a change of numéraire in the stochastic processes for risks sources, thus providing estimates under the forward risk-neutral measure that result in a gain in accuracy. We then parallelize the Monte Carlo method to speed-up the simulation process.

Optimal asset allocation for a general portfolio of life insurance policies

Asset liability matching remains an important topic in life insurance research. The objective of this paper is to find an optimal asset allocation for a general portfolio of life insurance policies. Using a multi-asset model to investigate the optimal asset allocation of life insurance reserves, this study obtains formulae for the first two moments of the accumulated asset value. These formulae enable the analysis of portfolio problems and a first approximation of optimal investment strategies. This research provides a new perspective for solving both single-period and multiperiod asset allocation problems in application to life insurance policies. The authors obtain an efficient frontier in the case of single-period method; for the multiperiod method, the optimal asset allocation strategies can differ considerably for different portfolio structures.

A general asset–liability management model for the efficient simulation of portfolios of life insurance policies

New regulations and a stronger competition have increased the importance of stochastic asset–liability management (ALM) models for insurance companies in recent years. In this paper, we propose a discrete time ALM model for the simulation of simplified balance sheets of life insurance products. The model incorporates the most important life insurance product characteristics, the surrender of contracts, a reserve-dependent bonus declaration, a dynamic asset allocation and a two-factor stochastic capital market. All terms arising in the model can be calculated recursively which allows an easy implementation and efficient simulation. Furthermore, the model is designed to have a modular organization which permits straightforward modifications and extensions to handle specific requirements. In a sensitivity analysis for sample portfolios and parameters, we investigate the impact of the most important product and management parameters on the risk exposure of the insurance company and show that the model captures the main behaviour patterns of the balance sheet development of life insurance products.

Acquiring Life Insurance Portfolios

Though the secondary market for life insurance policies has only recently developed, institutional investors and others involved in the life settlement industry are witnessing early signs of a tertiary market for whole portfolios of life insurance policies that have been formed over the past several years through multiple life settlement transactions. For institutional investors that are seeking either new investment opportunities or to diversify their existing investment portfolios, a tertiary market for portfolios of life insurance policies may present new investment opportunities and a means to minimize risk in a new class of investment assets. This article explains certain risks associated with the purchase of life insurance portfolios such as contestability risk and uncertain availability and quality of information on individual policies. The authors explain how life settlement providers can be helpful in the securitization of life settlement portfolios. They anticipate significant growth over the next several years in the tertiary market for life insurance portfolios.

“Authors’ Reply: Financial and Demographic Risks of a Portfolio of Life Insurance Policies with Stochastic Interest Rates: Evaluation Methods and Applications,” Maria Giuseppina Bruno, Emanuela Camerini and Alvaro Tomassetti, October 2000 - Discussion by Fabrizio Cacciafesta

“Authors’ Reply: Financial and Demographic Risks of a Portfolio of Life Insurance Policies with Stochastic Interest Rates: Evaluation Methods and Applications,” Maria Giuseppina Bruno, Emanuela Camerini and Alvaro Tomassetti, October 2000 - Discussion by Fabrizio Cacciafesta

“Financial and Demographic Risk of a Portfolio of Life Insurance Policies with Stochastic Interest Rates: Evaluation Methods and Applications,” M. G. Bruno, E. Camerini, and A. Tomassetti, October 2000

“Financial and Demographic Risk of a Portfolio of Life Insurance Policies with Stochastic Interest Rates: Evaluation Methods and Applications,” M. G. Bruno, E. Camerini, and A. Tomassetti, October 2000

Financial and Demographic Risks of a Portfolio of Life Insurance Policies with Stochastic Interest Rates

We refer to a recent paper by G. Parker (1997) in which the risk of a portfolio of life insurance policies (namely the risk related to the entire contractual life) is studied by separating the demographic component from the financial component. In our paper, after making a brief summary of Parker’s model, we propose two additional contributions: 1. We first give the problem a different formalization, thus allowing a portfolio risk analysis by management periods and a study of the risk due to the interactions among years; 2. We elaborate on a powerful and flexible algorithm for calculating the probability distribution of the sum of random variables that proves useful to solve not only the problems discussed in this paper concerning the risk analysis but also various other problems. In the paper, we also show, for both contributions, some applications made under the same financial and demographic assumptions taken by Parker; we also compare our results with Parker’s results.

On life insurance reserves in a stochastic mortality and interest rates environment

The calculation of the reserves in a stochastic mortality and interest rates environment for a general portfolio of life insurance policies is examined. The first two moments of the prospective loss random variable for the general portfolio are derived. A Monte Carlo simulation method is used to estimate the distribution of this random variable. Another approximation of the prospective loss random variable which is based on the assumption of a large portfolio is also considered. In the numerical examples, a discrete-time model for the stochastic interest rates is assumed.

One approach to dual randomness in life insurance. : Beekman J.A., Fuelling C.P., Scandinavian Actuarial Journal, nr. 2, 1993, pp. 173–182.

Abstract A model is presented which can be used when interest rates and future lifetimes are random, for life insurance. Expressions for the mean values and the standard deviations of a future life insurance payment are obtained. These can be used in determining contingency reserves and premium margins for possible adverse interest and mortality experience for a portfolio of life insurance policies. Four complete examples are considered, including four tables of values.

On the Exact Computation of the Aggregate Claims Distribution in the Individual Life Model

AbstractA recursive expression is derived for computing exactly the distribution of aggregate claims of a portfolio of life insurance policies. The recursion generalizes a formula of White and Greville for the claim numbers distribution and improves Kornya's approximation method for the aggregate claims distribution. It can be seen as the counterpart in the individual model of Panjer's recursion formula for the collective model.