Actuarial Liability Research Articles

Yield curve extrapolation with machine learning

Abstract Yield curve extrapolation to unobservable tenors is a key technique for the market-consistent valuation of actuarial liabilities required by Solvency II and forthcoming similar regulations. Since the regulatory method, the Smith–Wilson method, is inconsistent with observable yield curve dynamics, parsimonious parametric models, the Nelson–Siegel model and its extensions, are often used for yield curve extrapolation in risk management. However, it is difficult for the parsimonious parametric models to extrapolate yield curves without excessive volatility because of their limited ability to represent observed yield curves with a limited number of parameters. To extend the representational capabilities, we propose a novel yield curve extrapolation method using machine learning. Using the long short-term memory architecture, we achieve purely data-driven yield curve extrapolation with better generalization performance, stability, and consistency with observed yield curve dynamics than the previous parsimonious parametric models on US and Japanese yield curve data. In addition, our method has model interpretability using the backpropagation algorithm. The findings of this study prove that neural networks, which have recently received considerable attention in mortality forecasting, are useful for yield curve extrapolation, where they have not been used before.

Use of Constant Type Cost Prorate Method in Calculation of Actuarial Liability of Pension Funds

Use of Constant Type Cost Prorate Method in Calculation of Actuarial Liability of Pension Funds

Analysis of Changes in Total Actuarial Liabilities Using Projected Unit Credit Method

Analysis of Changes in Total Actuarial Liabilities Using Projected Unit Credit Method

COMPARISON OF PROJECTED UNIT CREDIT AND ENTRY AGE NORMAL METHODS IN PENSION FUND VASICEK AND COX-INGERSOLL-ROSS MODELS

The pension program is one of the pension fund's efforts to anticipate the risks that will be experienced by participants in old age. Actuarial calculations help to determine the benefits that participants will receive by considering life chances, interest rates, age when becoming a participant, and normal retirement age. This study aims to determine normal contributions and actuarial liabilities with the Projected Unit Credit and Entry Age Normal methods using stochastic interest rates, namely Vasicek and Cox-Ingersoll-Ross (CIR). The data used in this study are civil servants who work at the Natural Resources Management Office, Bulukumba Regency. The results of the calculation analysis showed that normal cost using the Projected Unit Credit (PUC) method with the Vasicek and Cox-Ingersoll-Ross (CIR) model interest rates increased as the length of service increased, and at the end of the working period the Cox-Ingersoll-Ross (CIR) model interest rate reached Rp14.773.176,- which was higher than Vasicek by Rp3.849.898,-. The results of the calculation of normal cost using the Entry Age Normal (EAN) method with the Vasicek model increase in the period 0-20 years of service, then decrease towards the contribution value at the beginning of the service period of Rp1.499.725,-. At the beginning of the working year, the normal cost using the Entry Age Normal method with the Cox-Ingersoll-Ross (CIR) model interest rate is Rp7.581.593,- then decreases for 24 years of service to Rp5.849.854,- after which it increases again towards the initial contribution value of the working year. The results of the calculation of actuarial liabilities show an increase as the length of service increases, for the Entry Age Normal (EAN) and Projected Unit Credit (PUC) methods with the Cox-Ingersoll-Ross (CIR) interest rate model at the end of the service period, it is found that both are the same value, namely Rp443.195.285,-. By using the Vasicek interest rate model for both methods, the same result is obtained at the end of the service period of Rp115.496.951,-. This shows that the actuarial liabilities for both methods used are affected by interest rates, and the Cox-Ingersoll-Ross (CIR) model is higher than Vasicek

Auditoria operacional dos sistemas previdenciários: achados do Tribunal de Contas do Estado do Ceará

The national public administration is preceded by being monitored and supervised given the large resources that are allocated to the provision of services that society needs, leaving the courts of accounts to their control and measurement. With regard to the management programs of the private pension systems, the courts began to audit actuarial management and the accounting entries referring to long-term provisions for the payment of retirement and pension benefits. The Federal Court of Auditors presented irregularities and the Court of Auditors of the State of Ceará carried out operational audits related to the municipal regimes, and asked: what were the findings of the operational audit? The answer came through research of an interpretive nature with a qualitative approach and a case study in two municipalities of the six audited. It was concluded that: the municipal social security management in the State is recurrent in the irregularities and vices in the processes of acquisition of goods, products, or services; actuarial estimates are defective and incapable of assessing the sustainability capacity of the social security system, with indications of the absence of adherence tests for the workforce, actuarial cash flow incompatible with future execution, and inconstancy in results; absence of recording mathematical provisions in the balance sheets, originating from actuarial estimates; and absence of projections of actuarial liabilities in the tax statements. The audits studied pointed out recommendations and determinations to managers, which must be monitored by the body with the possibility of sanctioning and returning resources to public coffers.

A defined benefit pension plan game with Brownian and Poisson jumps uncertainty

In this paper, we study the optimal management of an aggregated pension fund of defined benefit type by means of a differential game with two players, the firm and the participants. We assume that the fund wealth is greater than the actuarial liability and then the manager builds a pension fund surplus. In order to contemplate sudden changes in the financial market, the surplus can be invested in a portfolio with a bond and several risky assets where the uncertainty comes from Brownian motions and Poisson processes. The aim of the participants is to maximize a utility of the extra benefits. The game is analyzed in three scenarios. In the first, the aim of the firm is to maximize a utility of the fund surplus, in the second, to minimize the probability that the fund surplus reaches a low level, and in the third, to minimize the expected time of reaching a benchmark surplus. An infinite horizon is considered, and the game is solved by means of the dynamic programming approach. The influence of the jumps of the financial market on the Nash equilibrium strategies and the fund surplus is studied by means of a numerical illustration.

Pension Fund Calculation Using Projected Unit Credit, Entry Age Normal, and Attained Age Normal Method (Case Study : PT. Taspen (PERSERO) Cabang Pematang Siantar 2022)

Pension fund (pension plan) is the determination that the employer (company) provides benefits (payments) to employees after they retire for the services that provided while still working. The purpose of establishing a pension funds program is to fulfill the employer’s obligation, to guarantee the retirement period of the employees in the future, and to finance national development to create social welfare. In this study aim to determined normal costs and actuarial liabilities using the three methods consist of Projected Unit Credit (PUC) method, Entry Age Normal (EAN) method, and Attained Age Normal (AAN) method. The data used in this research is the information by PT. Taspen (Persero) Cabang Pematang Siantar such as date of birth, date of started work, basic salary, and the total of pension fund collected in the previous year. Otherwise, the data mortality rate of the employees from the 2022 employment mortality table (TMJ 2022) by PT. BPJS Ketenagakerjaan is also used. The result show that the best method for pension funds program in PT. TASPEN (Persero) Cabang Pematang Siantar is PUC method since the amount of unfunded actuarial liabilities (UAL) has the biggest difference between total actuarial liabilities and the amount that has been funded. It means that the pension funds program can give more surplus than the other methods.

PENGGUNAAN METODE PROJECTED UNIT CREDIT PADA ASURANSI PENSIUN GABUNGAN MODEL VASICEK DAN CIR

Pension plan is an investment plan offered by employee company or life insurance companies to help create retirement funds. This research attempts to estimate the normal cost that participants must pay as well as the actuarial liability that must be paid by the insurance company to the participants using Projected Unit Credit method. Projected Unit Credit method uses the present value of the pension benefit and divided it by participant’s years of service. stochastic interest such as the Vasicek model and the CIR model will be used as a comparison. The result of this research is that the estimation of the normal cost and actuarial liability with the CIR model is smaller than the Vasicek model in the initial year, but the CIR model experience a greater increase than the Vasicek model which causes the normal cost and actuarial liability with the CIR model more expensive than the Vasicek model at the end of the contract. Both premiums and the actuarial liabilities increase as participants age.

Pension Fund Calculation Using Traditional and Projected Unit Credit Methods for Total Actuarial Liability and Normal Cost Cases

The DSH Meat Kiosk is a kiosk that sells one of the foodstuffs, namely Beef. This DSH Meat Kiosk has been around for more than 20 years. However, as long as this kiosk is established, the manager still finds it difficult to analyze the profit from the sale. Therefore, this Profit and Loss Financial Statement is intended to assist traders in managing the profits generated. In this report a financial analysis is made in November 2021 and February 2022. The method used in making this report is to use primary data by collecting data in the form of interviews with kiosk owners relating to things needed in making profit and loss statements such as assets that owned, total revenue, operating costs and others. The results of this report show that sales in February 2022 decreased by 17.88% compared to November 2021. With this report, it is hoped that this report will help and make it easier to manage the profits generated and make decisions to generate the best profits.The discussion of the selected questions will look for what actuarial obligations are and what normal costs are based on the data provided. The purpose of this discussion is to know, understand, and be able to perform actuarial calculations regarding the unit credit method used. The unit credit method used is the traditional unit credit and the projected unit credit. The formula used for each question is as follows. andThe result of solving the first problem shows that the total actuarial liability on 1/1/95 is IDR 405,339.095. While the results of the second question show that the normal cost for 2021 on 1/1/2021 was IDR 1,071.43. From these results, users can find out how much actuarial obligations are and what normal costs are based on the data that has been provided.

Implementasi Metode Perhitungan Aktuaria Program Dana Pensiun Menggunakan Flask

The pension fund program is a program that seeks future planning by providing pension benefits to participants. The vital thing that becomes a concern in the pension fund program is the actuarial cost method. There are two categories for actuarial cost methods, which are Accrued Benefit-Cost Method and Projected Benefit-Cost Method. The normal contribution characteristic of the Projected Benefit-Cost Method is more stable than the Accrued Benefit-Cost Method, so it is better to use it from the participants’ perspective. This study discusses the use of the Projected Benefit-Cost Method by calculating normal contributions and actuarial liabilities from the methods included in it, which are Attained Age Normal, Entry Age Normal, and Individual Level Premium. Based on the calculation results, the Entry Age Normal and Individual Level Premium methods have a smaller final value of normal contribution payments and have a larger actuarial liability than the Attained Age Normal. Thus, of the three methods included in the Projected Benefit-Cost Method, the Entry Age Normal and Individual Level Premium methods are better used from the perspective of participants. For the calculation of pension funding using the Attained Age Normal, Entry Age Normal, and Individual Level Premium methods to be widely implemented by the public, this study created an application website using flask, which can be accessed at https://perhitunganaktuariadapen.herokuapp.com/.

Determining the Pension Benefit Obligation of a Defined Benefit Plan: Applying a Multivariate ARIMA Stochastic Model

<p>In this study we examine the robustness of fit for a multivariate and an autoregressive integrated moving average model to a data sample time series type. The sample is a recurrent actuarial data set for a 10-year horizon. We utilize this methodology to contrast with stochastic models to make projections beyond the data horizon. Our key results suggest that both types of models are useful for making predictions of actuarial liability levels given by PBO Projected Benefit Obligations on and off the horizon of the sample time series. As we have seen in prior research, the use of multivariate models for control and auditing purposes is widely recommended. Fast and reliable statistical estimates are desirable in all cases, whether for audit purposes or to verify and validate miscellaneous actuarial results.</p>

Abordagem direta para avaliar o ajuste de risco de acordo com a IFRS 17

ABSTRACT This paper aims to develop a method that can be adopted by insurers to assess the risk adjustment for nonfinancial risks (RA) required by International Financial Reporting Standards 17 (IFRS 17). Unlike other methods, the method proposed here directly returns the RA for each liability related to a group of insurance contracts: remaining coverage and incurred claims. Moreover, each portion of the RA is correctly allocated to the corresponding actuarial liability, which constitutes an advantage over other methods. The method follows IFRS 17 directives and contributes to standardize accounting practices of insurers around the world, thus increasing the degree of comparability between financial statements in different jurisdictions. This paper should be relevant for insurance companies, for insurance market supervisors and regulators, as well as for practitioners in general. The method takes advantage of the collective risk theory and of the Monte Carlo simulation technique to adjust probability distributions used to calculate two different loading factors that, when applied to the carrying amount of unearned premiums and to the expected present value of incurred claims, directly return the RA for each liability related to a group of insurance contracts: remaining coverage and incurred claims. Our results show that, for large-scale portfolios, the central limit theorem holds and the distributions used to assess the loading factors can be well approximated by the normal distribution. Additionally, the values obtained for each loading factor are small, which means that the RA is relatively low when compared to the carrying amount of unearned premiums and to the expected present value of incurred claims. This result is in line with the law of large numbers, which states that, for large-scale portfolios, the risk borne by the insurer becomes considerably lower, since it is easier to predict the behavior of aggregate future claims.

MODERNIZING PENSION FUND CONTRIBUTION

Purpose: The purpose of this research is to develop a pension model which uses mobile phone technology to facilitate contribution towards the user's pension scheme. Methodology: The entry age pension funding method, and annuity present value & accumulations methods are used to come up with the contribution rate and the actuarial liability for the model. Findings: The model developed is independent of salary or any other income and only takes into consideration those legally registered to use mobile phone. Being a private pension plan, and the fact that it involves the member directly via and individual mobile phone subscription, wider coverage is anticipated. Unique contribution to theory, practice and policy: Contribution towards pension scheme by use of mobile phone technology in which contribution (which is fixed and independent of salary) is achieved by how frequently, the credit is loaded and used by the subscriber.

Total Actuarial Liabilities and Normal Costs Using The Unit Credit Method

The pension fund program requires an actuarial calculation, such as the amount of actuarial obligations and normal costs for each pension fund participant. Total actuarial liabilities are calculated to show the company's liability for pension benefits for pension fund participants. Funding in pension funds is obtained from the normal costs or contributions paid by participants to the pension fund. By using the unit credit method, the total value of actuarial liabilities at 1/1/2020 is IDR 405,338.5. Then by using the unit credit method, it is projected that the normal cost on 1/1/2019 is IDR 1,071.43. The calculation method on funding aims to ensure that the collected pension plan funds will be sufficient to pay pension benefits to participants when they retire.

Calculation of Pension Funds Using the Unit Credit Method

Everyone certainly wants a welfare in the future, including employees. The company provides a pension program as a form of the company's concern for its employees. This pension fund provides pension benefits to employees at the time of retirement. Funding for this pension requires actuarial calculations which are normal costs and actuarial obligations. This discussion aims to calculate the amount of normal costs and actuarial obligations that must be incurred. The method used in this discussion is the ordinary credit unit method and projecting credit units by analyzing the use of actuarial formulas from several literature studies. In the first discussion using the ordinary credit unit method, the total actuarial liability on 1/1/95 is IDR. 405,355, while in the second discussion using the projecting credit unit method, the normal cost for 1994 on 1/1/94 is IDR 1071, 42. It is hoped that this discussion can increase the reader's knowledge of pension fund mathematics, especially to determine normal costs and also the value of actuarial obligations using the ordinary credit unit method or the projecting credit unit method.

Mean-variance investment and contribution decisions for defined benefit pension plans in a stochastic framework

<p style='text-indent:20px;'>In this paper we investigate the management of a defined benefit pension plan under a model with random coefficients. The objective of the pension sponsor is to minimize the solvency risk, contribution risk and the expected terminal value of the unfunded actuarial liability. By measuring the solvency risk in terms of the variance of the terminal unfunded actuarial liability, we formulate the problem as a mean-variance problem with an additional running cost. With the help of a system of backward stochastic differential equations, we derive a time-consistent equilibrium strategy towards investment and contribution rate. The obtained equilibrium strategy turns out to be a good candidate for a stable contribution plan. When the interest rate is given by the Vasicek model and all other coefficients are deterministic, we obtain closed-form solutions of the equilibrium strategy and efficient frontier.

Using Expected Geometric Values to Calculate the Cost of Interest in Hyper-inflationary Environments: the Case of Venezuela

It is of vital importance to explore the relationship between pensions and inflationary levels because this forms a link between social policy and economic development in the context of Venezuela’s challenging economy and its impact on the development of pension systems. With such rampant inflation, companies must adjust the rates of salary increases to avoid a significant decrease in the purchasing power of income from defined benefit plans. Our research seeks to find the possibility of using an average geometric rate of future interest rates expressed as an expected value to discount obligations. Consequently, the cost of interest associated with the actuarial liability of the Benefit plans increases substantially in the next fiscal period to the actuarial valuation, sometimes compromising its sustainability over time. In order to minimize this problem, two scenarios for calculating the interest rate are proposed to smooth out this volatile effect; both are based on a geometric average with the expectation of working life or with the duration of the obligations. We are careful to use a reasonable interest rate that is not so high as to compromise the cash flow, resulting in skewed annual results of the companies. Our research seeks to find the possibility of using an average geometric rate of future interest rates expressed as an expected value to discount obligations. We formulate and actuarially evaluate two different scenarios, based on job expectations and Macaulay's duration, of the obligations that allow the sustainability of the plan in an environment of extremely high inflation. To illustrate the impact of the basic annual expenditure of the period, the results of an actuarial valuation of an actual Venezuelan company were utilized. Despite some companies adjusting their book reserves increasingly through a geometric progression, the amounts associated with the costs of interest would be huge in any such adjustment pattern. Therefore, we suggest adoption of one of the alternatives described in the research.

Valuation of Actuarial Liability Using Markov

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Using Multivariant Regression Analysis to Compute Longevity Risk and Actuarial Liability: The Case of Social Benefits for Workers in Venezuela

In this study, a multivariate regression model is determined that allows computation of the actuarial liability of social benefits using a group of potential predictors. In general, the previous or independent predictors are the same as those utilized in an actuarial valuation of labor commitments. Several linear and non-linear models are considered and tested in this study. Among the most important findings of this research is that the PBO or Actuarial Liability depends fundamentally on a linear basis of two fundamental variables in the quantification of Social Benefits -- the Guarantees and the Social Benefits to Pay (PSP). The attractiveness of a relatively simple yet structurally robust model is a very attractive option in situations where managers are tasked to provide estimates in relatively short order, given that the two variables highlighted are generally readily available for most organizations. Realistically, companies are often required to give quick estimates, and they find it quite difficult to quantify an order of this magnitude. This model succeeds in filling this informational gap at the 4 percent interest rate.

Market risk based capital for Brazilian insurance companies: A stochastic approach☆

Solvency II defines minimum capital requirements from insurance companies, due to their exposure to risk. Regulatory bodies of the Brazilian insurance market issued regulations based on a deterministic model for the calculation of risk based capital. In this study, we discuss a simple alternative stochastic model that may be more adequate to measure the minimum capital, based on an asset and liability management mechanism. By allowing the estimation of a probability distribution of losses, the model is useful to identify not only average results but also extreme results for the portfolio. Focusing on the market risk associated with interest rate exposures, we apply a stochastic model to investigate risks from a pension plan product of an insurance company operating in Brazil. The Brazilian case is relevant, since due to its high interest rate levels, high interest volatility and the usual investment in inflation–index bonds, deterministic models can poorly reflect the effective risk exposure of insurers. For the analysis of the actuarial liabilities, we use demographic data from the insurer. For the analysis of the assets, we investigate different hypothetical portfolios of investments in government bonds, analyzing how interest rates changes and indexes mismatch impact the potential loss. The results of the simulation of the stochastic model, for all scenarios, show potential losses that are substantially higher than the values established by the regulatory model. Estimate of potential loss can reach differences of up to 419%. The results suggest that the deterministic model defined by the regulatory agencies may be a fragile reference to the real capital needs of an insurance company, especially when considering the economic environment of emerging countries.