Modelling Outstanding Claims with Mixed Compound Processes in Insurance

In general insurance, measuring the uncertainty of future loss payments and estimating the claims reserve are primary goals of actuaries. To deal with these tricky tasks, a broad literature is available on deterministic and stochastic approaches, most of which aims at straightforwardly modelling the overall claims reserve. In this paper by an extended, very general and reproducible case-study, we analyze the reserving process by attributing to each cell of the lower part of the run-off triangle a Compound mixed Poisson Process, calibrated upon both the numbers of claims and future average costs and considering as well the dependence among incremental claims. We provide analytically the moments of both incremental payments and the total reserve. Furthermore, we accordingly consider the probability distribution of the claims reserve, which is necessary for the assessment of the Risk Reserve capital requirement in a Solvency II framework. To test the impact of the model under different scenarios, insurers and lines of business, the case study is thoroughly analyzed by exploiting the Fisher-Lange average cost method.

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A CORRELATION SENSITIVITY ANALYSIS OF NON-LIFE UNDERWRITING RISK IN SOLVENCY CAPITAL REQUIREMENT ESTIMATION

Astin Bulletin ◽

10.1017/asb.2012.1 ◽

2013 ◽

Vol 43 (1) ◽

pp. 21-37 ◽

Cited By ~ 3

Author(s):

Lluís Bermúdez ◽

Antoni Ferri ◽

Montserrat Guillén

Keyword(s):

Sensitivity Analysis ◽

Solvency Ii ◽

Capital Requirement ◽

Solvency Capital Requirement ◽

The Standard Model ◽

Solvency Capital ◽

One Year ◽

The Impact ◽

Model Approach

AbstractThis paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the solvency capital requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the standard model approach. Alternatively, the requirement is then calculated using an internal model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR, we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

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Mortality data reliability in an internal model

Annals of Actuarial Science ◽

10.1017/s1748499520000081 ◽

2020 ◽

Vol 14 (2) ◽

pp. 420-444

Author(s):

Fabrice Balland ◽

Alexandre Boumezoued ◽

Laurent Devineau ◽

Marine Habart ◽

Tom Popa

Keyword(s):

Data Quality ◽

Internal Model ◽

Mortality Rates ◽

Solvency Ii ◽

West Germany ◽

Mortality Data ◽

Longevity Risk ◽

Capital Requirement ◽

Stochastic Mortality ◽

The Impact

AbstractIn this paper, we discuss the impact of some mortality data anomalies on an internal model capturing longevity risk in the Solvency 2 framework. In particular, we are concerned with abnormal cohort effects such as those for generations 1919 and 1920, for which the period tables provided by the Human Mortality Database show particularly low and high mortality rates, respectively. To provide corrected tables for the three countries of interest here (France, Italy and West Germany), we use the approach developed by Boumezoued for countries for which the method applies (France and Italy) and provide an extension of the method for West Germany as monthly fertility histories are not sufficient to cover the generations of interest. These mortality tables are crucial inputs to stochastic mortality models forecasting future scenarios, from which the extreme 0.5% longevity improvement can be extracted, allowing for the calculation of the solvency capital requirement. More precisely, to assess the impact of such anomalies in the Solvency II framework, we use a simplified internal model based on three usual stochastic models to project mortality rates in the future combined with a closure table methodology for older ages. Correcting this bias obviously improves the data quality of the mortality inputs, which is of paramount importance today, and slightly decreases the capital requirement. Overall, the longevity risk assessment remains stable, as well as the selection of the stochastic mortality model. As a collateral gain of this data quality improvement, the more regular estimated parameters allow for new insights and a refined assessment regarding longevity risk.

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Environmental Run-off Impact Case Study: The Impact of Development and Campus Development of State Islamic University (UIN) Malang

Natural-B ◽

10.21776/ub.natural-b.2011.001.02.2 ◽

2011 ◽

Vol 1 (2) ◽

pp. 102-109

Author(s):

Mohammad Nawawi ◽

Bambang Rahadi

Keyword(s):

Run Off ◽

The Impact

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Comparing Solvency II and Life and General Insurance Capital approaches to capital determination of a life portfolio in the presence of stress scenarios

Annals of Actuarial Science ◽

10.1017/s1748499518000027 ◽

2018 ◽

Vol 13 (1) ◽

pp. 36-66

Author(s):

Kangjing Tan ◽

Aaron Bruhn

Keyword(s):

Risk Management ◽

Solvency Ii ◽

Capital Requirements ◽

Life Insurers ◽

General Insurance ◽

Pillar Structure ◽

Matching Adjustment ◽

The Impact ◽

Capital Intensive

AbstractThe European-centric Solvency II and Australian-centric Life and General Insurance Capital regimes are two examples of risk-based approaches to capital determination and risk management for life insurers. Both consist of a three-pillar structure covering capital, risk management and disclosure requirements. We apply the capital requirements of each regime to three synthetic sets of insurance policies, including a risk, annuity and combined portfolios, and consider the impact on capital arising from three separate and relatively severe stress events. Results highlight the relatively capital intensive nature of annuities, the differences between different capital regimes, the significance of solvency II’s matching adjustment and the robustness of each regime to both pandemic and economic stresses. Results also highlight the nature of diversification benefits from within each capital regime, on overall capital requirements.

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Factors impacting community’s prioritization towards the benefits of Sustainable Urban Drainage Systems: A case study of Nhieu Loc – Thi Nghe sub-basin, Ho Chi Minh City

Science & Technology Development Journal - Social Sciences & Humanities ◽

10.32508/stdjssh.v4i4.604 ◽

2020 ◽

Vol 4 (4) ◽

pp. First

Author(s):

Nguyen Hoang My Lan ◽

Ho Huu Loc ◽

Phan Dinh Bich Van ◽

Vo Le Phu ◽

Le Van Trung

Keyword(s):

Statistical Tests ◽

Drainage System ◽

Impact Factors ◽

Urban Drainage ◽

Run Off ◽

Spss Software ◽

The Impact ◽

Priority Levels ◽

Data Processing Methods

Sustainable Urban Drainage System (SUDS) includes various drainage techniques designed to reduce the run-off flow, improve the water quality, and provide amenity or landscape features. However, selecting the appropriate SUDS technique depends on not only the technical characteristics but also the community's perception and preference. Therefore, this study aims to determine the impact factors on the probability of households' prioritization towards SUDS benefits in the context of Nhieu Loc - Thi Nghe sub-basin, including the benefits of flood reduction, environmental enhancement, and landscape improvement. Data processing methods used in this study consist of statistical tests and ordinal regression using SPSS software. The regression results show that the overall accurate prediction rate for the 3 priority levels of SUDS benefits ranges from 50% to 70%. Factors that statistically significantly influence the priority include household income, knowledge of SUDS, frequency of flooding, depth of flooding, the distance to the nearest park, the distance to the nearest water body, and the distance to the nearest flooded location. In particular, the proximity to the nearest park affects the priority choice for all SUDS benefits with the principle that households near the park will probably choose higher priority to SUDS benefits than those living further.

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A Bridge between Local GAAP and Solvency II Frameworks to Quantify Capital Requirement for Demographic Risk

Risks ◽

10.3390/risks9100175 ◽

2021 ◽

Vol 9 (10) ◽

pp. 175

Author(s):

Gian Paolo Clemente ◽

Francesco Della Corte ◽

Nino Savelli

Keyword(s):

Life Insurance ◽

Random Variable ◽

Mortality Rates ◽

Solvency Ii ◽

Capital Requirement ◽

Insurance Contracts ◽

Financial Conditions ◽

Accounting Principles ◽

Demographic Risk

The aim of this paper is to provide a stochastic model useful for assessing the capital requirement for demographic risk in a framework coherent with the Solvency II Directive. The model extends to the market consistent context classical methodologies developed in a local accounting framework. The random variable demographic profit, defined in literatue under local accounting principles, is indeed analysed in a Solvency II framework. We provide a unique formulation for different non-participating life insurance contracts and we prove analytically that the valuation of demographic profit can be significantly affected by the financial conditions in the market. Regarding this topic, we implement the Vašíček model to add randomness to risk-free rates. A case study has also been developed considering a portfolio of life insurance contracts. Results prove the effectiveness of the model in highlighting the main drivers of capital requirement evaluation (e.g., the volatility of both mortality rates and risk-free rates), also compared to the local GAAP framework.

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