JournalTOCs

European Actuarial Journal
Journal Prestige (SJR): 0.459

Citation Impact (citeScore): 1
Number of Followers: 0

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2190-9733 - ISSN (Online) 2190-9741
Published by Springer-Verlag

[2469 journals]

Generalized PELVE and applications to risk measures
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  Abstract: Abstract The continuing evolution of insurance and banking regulation has raised interest in the calibration of different risk measures associated with suitable confidence levels. In particular, Li and Wang (2019) have introduced a probability equivalent level (called PELVE) for the replacement of Value at Risk (VaR) with Conditional Value at Risk (CVaR). Extending their work, we propose two generalizations of PELVE that combine useful theoretical properties with empirical benefits in risk analysis. The former, termed d-PELVE, establishes a correspondence between VaR and suitably parameterized distortion risk measures. The latter, termed g-PELVE, iterates the construction of CVaR starting from VaR to a general coherent risk measure. We state conditions for the existence and uniqueness of the proposed measures and derive additional properties for specific classes of underlying risk functionals. A study of Generalized Pareto Distributions reveals an interesting correspondence between PELVE and g-PELVE, and explores their relationship with the tail index. An empirical application illustrates the usefulness of (g-)PELVE in characterizing tail behavior not only for individual asset returns, but also for possible portfolio combinations.
  PubDate: 2022-06-29
Smooth projection of mortality improvement rates: a Bayesian
two-dimensional spline approach
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  Abstract: Abstract This paper proposes a spline mortality model for generating smooth projections of mortality improvement rates. In particular, we follow the two-dimensional cubic B-spline approach developed by Currie et al. (Stat Model 4(4):279–298, 2004), and adopt the Bayesian estimation and LASSO penalty to overcome the limitations of spline models in forecasting mortality rates. The resulting Bayesian spline model not only provides measures of stochastic and parameter uncertainties, but also allows external opinions on future mortality to be consistently incorporated. The mortality improvement rates projected by the proposed model are smoothly transitioned from the historical values with short-term trends shown in recent observations to the long-term terminal rates suggested by external opinions. Our technical work is complemented by numerical illustrations that use real mortality data and external rates to showcase the features of the proposed model.
  PubDate: 2022-06-27
Impact of rough stochastic volatility models on long-term life insurance
pricing
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  Abstract: Abstract The Rough Fractional Stochastic Volatility (RFSV) model of Gatheral et al. (Quant Financ 18(6):933–949, 2014) is remarkably consistent with financial time series of past volatility data as well as with the observed implied volatility surface. Two tractable implementations are derived from the RFSV with the rBergomi model of Bayer et al. (Quant Financ 16(6):887–904, 2016) and the rough Heston model of El Euch et al. (Risk 84–89, 2019). We now show practically how to expand these two rough volatility models at larger time scales, we analyze their implications for the pricing of long-term life insurance contracts and we explain why they provide a more accurate fair value of such long-term contacts. In particular, we highlight and study the long-term properties of these two rough volatility models and compare them with standard stochastic volatility models such as the Heston and Bates models. For the rough Heston, we manage to build a highly consistent calibration and pricing methodology based on a stable regime for the volatility at large maturity. This ensures a reasonable behavior of the model in the long run. Concerning the rBergomi, we show that this model does not exhibit a realistic long-term volatility with extremely large swings at large time scales. We also show that this rBergomi is not fast enough for calibration purposes, unlike the rough Heston which is highly tractable. Compared to standard stochastic volatility models, the rough Heston hence provides efficiently a more accurate fair value of long-term life insurance contracts embedding path-dependent options while being highly consistent with historical and risk-neutral data.
  PubDate: 2022-06-25
Editorial
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  PubDate: 2022-06-02
Correction to: Current developments in German pension schemes: What are
the benefits of the new target pension'
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  PubDate: 2022-06-01
Rule-based strategies for dynamic life cycle investment
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  Abstract: Abstract In this work, we consider rule-based investment strategies for managing a defined contribution pension savings scheme, under the Dutch pension fund testing model. We find that dynamic, rule-based investment strategies can outperform traditional static strategies, by which we mean that the investor may achieve the target retirement income with a higher probability or limit the shortfall when the target is not met. In comparison with dynamic programming-based strategies, the rule-based strategies have more stable asset allocations throughout time and avoid excessive transactions that may be hard to explain to an investor. We also study a combined strategy of a rule-based target with dynamic programming. A key feature of our setting is that there is no risk-free asset, instead, a matching portfolio is introduced for the investor to avoid unnecessary risk.
  PubDate: 2022-06-01
Modern tontines as a pension solution: a practical overview
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  Abstract: Abstract In the context of global aging population, improved longevity and ultra-low interest rates, the question of pension plan under-funding and adequate elderly financial planning is gaining awareness worldwide, both among experts, regulatory bodies, and popular media. Additional emergence of societal changes—Peer to Peer business model and Financial Disintermediation—have contributed to the resurgence of the concept of “Tontines” in various papers and the proposal of further models. These generalizations can offer efficient decumulation schemes with high longevity protection which is particularly well adapted for retirement needs—both for its members and carriers. In this paper, we revisit the mechanism proposed by Fullmer and Sabin (Journal of Accounting and Finance, 2019. https://doi.org/10.33423/jaf.v19i8.2615)—which allows the pooling of Modern Tontines through a self-insured community. This “Tontine” generalization retains the flexibility of an individual design: open contribution for a heterogeneous population, individualized asset allocation and predesigned annuitization plan. The actuarial fairness is achieved by allocating the deceased proceedings to survivors using a specific individual pool share which is a function of the prospective expected payouts for the period considered. After a brief introduction, this article provides a formalization of the mathematical framework with prospective analysis, characterizes the inherent bias, generalizes the mechanism to joint lives, and analyses simulated outcomes based on various assumptions. A reverse moral hazard limit is exposed and discussed (the “Term Dilemma”). Some solutions are then proposed to overcome scheme shortcomings and some requirements for practical implementation are discussed.
  PubDate: 2022-06-01
A comprehensive model for cyber risk based on marked point processes and
its application to insurance
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  Abstract: Abstract After scrutinizing technical, legal, financial, and actuarial aspects of cyber risk, a new approach for modelling cyber risk using marked point processes is proposed. Key covariates, required to model frequency and severity of cyber claims, are identified. The presented framework explicitly takes into account incidents from malicious untargeted and targeted attacks as well as accidents and failures. The resulting model is able to include the dynamic nature of cyber risk, while capturing accumulation risk in a realistic way. The model is studied with respect to its statistical properties and applied to the pricing of cyber insurance and risk measurement. The results are illustrated in a simulation study.
  PubDate: 2022-06-01
A bias-corrected Least-Squares Monte Carlo for solving multi-period
utility models
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  Abstract: Abstract The Least-Squares Monte Carlo (LSMC) method has gained popularity in recent years due to its ability to handle multi-dimensional stochastic control problems, including problems with state variables affected by control. However, when applied to the stochastic control problems in the multi-period expected utility models, such as finding optimal decisions in life-cycle expected utility models, the regression fit tends to contain errors which accumulate over time and typically blow up the numerical solution. In this paper we propose to transform the value function of the problems to improve the regression fit, and then using either the smearing estimate or smearing estimate with controlled heteroskedasticity to avoid the re-transformation bias in the estimates of the conditional expectations calculated in the LSMC algorithm. We also present and utilise recent improvements in the LSMC algorithms such as control randomisation with policy iteration to avoid accumulation of regression errors over time. Presented numerical examples demonstrate that transformation method leads to an accurate solution. In addition, in the forward simulation stage of the control randomisation algorithm, we propose a re-sampling of the state and control variables in their full domain at each time t and then simulating corresponding state variable at \(t+1\) , to improve the exploration of the state space that also appears to be critical to obtain a stable and accurate solution for the expected utility models.
  PubDate: 2022-06-01
Pricing participating longevity-linked life annuities: a Bayesian Model
Ensemble approach
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  Abstract: Abstract Participating longevity-linked life annuities (PLLA) in which benefits are updated periodically based on the observed survival experience of a given underlying population and the performance of the investment portfolio are an alternative insurance product offering consumers individual longevity risk protection and the chance to profit from the upside potential of financial market developments. This paper builds on previous research on the design and pricing of PLLAs by considering a Bayesian Model Ensemble of single population generalised age-period-cohort stochastic mortality models in which individual forecasts are weighted by their posterior model probabilities. For the valuation, we adopt a longevity option decomposition approach with risk-neutral simulation and investigate the sensitivity of results to changes in the asset allocation by considering a more aggressive lifecycle strategy. We calibrate models using Taiwanese (mortality, yield curve and stock market) data from 1980 to 2019. The empirical results provide significant valuation and policy insights for the provision of a cost effective and efficient risk pooling mechanism that addresses the individual uncertainty of death, while providing appropriate retirement income and longevity protection.
  PubDate: 2022-06-01
An optimal reinsurance simulation model for non-life insurance in the
Solvency II framework
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  Abstract: Abstract In this paper, we propose an approach to explore reinsurance optimization for a non-life multi-line insurer through a simulation model that combines alternative reinsurance treaties. Based on the Solvency II framework, the model maximises both solvency ratio and portfolio performance under user-defined constraints. Data visualisation helps understanding the numerical results and, together with the concept of the Pareto frontier, supports the selection of the optimal reinsurance program. We show in the case study that the methodology can be easily restructured to deal with multi-objective optimization, and, finally, the selected programs from each proposed problem are compared.
  PubDate: 2022-06-01
Bounds on Spearman’s rho when at least one random variable is
discrete
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  Abstract: Abstract Spearman’s rho is one of the most popular dependence measures used in practice to describe the association between two random variables. However, in case of at least one random variable being discrete, Spearman’s correlations are often bounded and restricted to a sub-interval of \([-1,1]\) . Hence, small positive values of Spearman’s rho may actually support a strong positive dependence when getting close to its highest attainable value. Similarly, slight negative values of Spearman’s rho can actually mean a strong negative dependence. In this paper, we derive the best-possible upper and lower bounds for Spearman’s rho when at least one random variable is discrete. We illustrate the obtained lower and upper bounds in some situations of practical relevance.
  PubDate: 2022-06-01
Socio-economic differentiation in experienced mortality modelling and its
pricing implications
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  Abstract: Abstract In recent years, increasing availability and quality of the portfolio data enables the life insurers to render fair and flexible pricing based on individual-level socio-economic attributes. Yet, many insurers price based on the “experience factor”; portfolio-specific mortality divided by population mortality. We incorporate the logistic regression in the experience mortality model by Plat (Insurance 45:123–132, 2009) and examine the effect of the differentiating factor(s) on the level and trend of mortality. The regression model accounts for socio-economic factors, such as salary, in the portfolio and constructs the corresponding differentiated experience factors. To address the varying uncertainty in each class of the differentiated experienced mortality, we provide the price of a simple survival benefit for a cohort with and without differentiation. We employ the EIOPA risk-margin price to examine how the differentiated mortality can be reflected in the required risk-loading, using the salary as an example differentiator. Further, we extend the risk margin price to a “time-consistent” price to address the considerable likelihood of the middle-time dynamics of the experience mortality in long-dated contracts. The Least Square Monte Carlo (LSMC) method serves as the numerical method to calculate the conditional operators in the time-consistent price. We find that differentiation is significant for different salary classes. For example, for the 40 years old male cohort, salary differentiation can result in around 7% discount for the low salary class and 7.9% surcharge for the high salary class.
  PubDate: 2022-06-01
Best upper and lower bounds on Spearman’s rho for zero-inflated
continuous variables and their application to insurance
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  Abstract: Abstract In this note, we establish the best lower and upper bounds on Spearman’s rho for zero-inflated continuous random variables studied by Pimentel (Kendall’s Tau and Spearman’s Rho for Zero Inflated Data (Ph.D. dissertation). Western Michigan University, Kalamazoo, 2009). The proposed bounds are explicitly expressed in terms of the respective probability masses at the origin. As illustrated in an example based on insurance data, these bounds are useful in practice when interpreting the values of Spearman’s rho.
  PubDate: 2022-06-01
Practical partial equilibrium framework for pricing of mortality-linked
instruments in continuous time
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  Abstract: Abstract This work considers a partial equilibrium approach for pricing longevity bonds in a stochastic mortality intensity setting. Thus, the pricing methodology developed in this work is based on a foundational economic principle and is realistic for the currently illiquid life market. Our model consists of economic agents who trade in risky financial security and longevity bonds to maximize the monetary utilities of their trades and income. Stochastic mortality intensity affects agents’ income, resulting in market incompleteness. The longevity bond introduced acts as a hedge against mortality risk, and we prove that it completes the market. From a practical perspective, we characterize and compute the endogenous equilibrium bond price. In a realistic setting with two agents in a transaction, numerical experiments confirm the expected intuition of price dependence of model parameters.
  PubDate: 2022-06-01
A general framework for analysing the mortality experience of a large
portfolio of lives: with an application to the UK universities
superannuation scheme
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  Abstract: Abstract We propose a general framework that can be used to analyse the mortality experience of a large portfolio of lives. The objective of the framework is to provide a firm evidence base to support the setting of future mortality assumptions for the portfolio as a whole or subgroup-by-subgroup. The framework is developed in tandem with an analysis of the mortality of pensioners in the Universities Superannuation Scheme (USS), the largest funded pension scheme in the UK and one with a highly educated and very homogeneous membership. The USS experience was compared with English mortality subdivided into deprivation deciles using the Index of Multiple Deprivation (IMD). USS was found to have significantly lower mortality rates than even IMD-10 (the least deprived of the English deciles), but with similar mortality improvement rates to that decile over the period 2005–2016. Higher pensions were found to predict lower mortality, but only weakly so, and only for persons who retired on the first day of a month (mostly from active service). We found that other potential covariates derived from an individual’s post/zip code (geographical region and the IMD associated with their local area) typically had no explanatory power. This lack of dependence is an important conclusion of the USS-specific analysis and contrasts with others that consider the mortality of more heterogeneous scheme memberships. Although the key findings are likely to be particular to USS, we argue that our analytical framework will be useful for other large pension schemes and life annuity providers.
  PubDate: 2022-04-29
Discussion on ‘A comprehensive model for cyber risk based on marked
point processes and its applications to insurance’ (Zeller, Scherer)
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  PubDate: 2022-04-27
Discussion on “Premium rating without losses” (M. Fackler)
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  PubDate: 2022-03-31
  DOI: 10.1007/s13385-022-00310-8
Premium rating without losses
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  Abstract: Abstract In insurance and even more in reinsurance it occurs that about a risk you only know that it has suffered no losses in the past, e.g. seven years. Some of these risks are furthermore such particular or novel that there are no similar risks to infer the loss frequency from. In this paper we propose a loss frequency estimator that copes with such situations, by just relying on the information coming from the risk itself: the “amended sample mean”. It is derived from a number of practice-oriented first principles and turns out to have desirable statistical properties. Some variants are possible, enabling insurers to align the method to their preferred business strategy, by trading off between low initial premiums for new business and moderate premium increases after a loss for renewal business. We further give examples where it is possible to assess the average loss from some market or portfolio information, such that overall one has an estimator of the risk premium.
  PubDate: 2022-01-24
  DOI: 10.1007/s13385-021-00302-0
Efficient evaluation of alternative reinsurance strategies using control
variates
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  Abstract: Abstract In this short communication, we present a new, simple control-variate Monte Carlo procedure for enhancing the evaluation accuracy of alternative reinsurance strategies that an insurance company might adopt.
  PubDate: 2022-01-20
  DOI: 10.1007/s13385-022-00304-6