Actuarial Principles Research Articles

Epidemiological and Health Insurance Models for a Communicable Disease

This paper considers an epidemiological model, referred to as SEIDRS disease model design for a communicable disease insurance policy. Epidemiologically, the individual population has five demographic groups, which includes: susceptibles (S), exposed (E), infectives undergoing treatments (I), infectives but dead (D) and (R) infectives but recovered from the communicable disease as stipulated in the insurance policy. The latter rejoined the susceptible group and then, continues with the insurance company by paying premium until such insured becomes infected again. The class of infectives comprises a union of those groups that are under treatment and the dead policy holders (PHs). The susceptible and exposed individuals constantly face the risks of being infected by the disease, while the infective class faces the risks of death resulting from the disease. Again, the probability function of a PH to remain susceptible under the SEIDRS disease model is considered, in this paper. Consequently, we obtain, for the insurance policy, the probability density function and cumulative distribution function under the SEIDRS disease model. Using the actuarial principles and techniques, we determine the parties’ insurance financial obligations as well as the insurance quantities. Some empirical results arising from the model analyses, in this paper are considered.

Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation

ABSTRACT This paper introduces new valuation schemes called actuarial-consistent valuations for insurance liabilities which depend on both financial and actuarial risks, which imposes that all actuarial risks are priced via standard actuarial principles. We propose to extend standard actuarial principles by a new actuarial-consistent procedure, which we call ‘two-step actuarial valuations’. In the case valuations are coherent, we show that actuarial-consistent valuations are equivalent to two-step actuarial valuations. We also discuss the connection with ‘two-step market-consistent valuations’ from Pelsser, A. & Stadje, M. [(2014). Time-consistent and market-consistent evaluations. Mathematical Finance 24(1), 25–65]. In particular, we discuss how the dependence structure between actuarial and financial risks impacts both actuarial-consistent and market-consistent valuations.

Research on the Risk Measurement Algorithm of Supply Chain Order Financing Based on Insurance Actuarial

In today’s globalized economy, all the links of supply chain are interlinked. Most of the upstream raw material manufacturers or producers in the said chain are small- and medium-sized enterprises (SMEs) that provide the basis for the efficient operation of the whole supply chain. However, SMEs in China, especially those playing a pivotal role in China’s export-oriented economy at this stage, do not have access to the corresponding financial treatment. Supply chain finance provides a new perspective to solve this contradiction. Henceforth, this paper introduces modern financial engineering risk measurement tools to measure the financial risk in supply chain finance, specifically while evaluating the single financing business. Moreover, the chief objective of this paper will be the analysis of the characteristics and connotations of order financing business model. In addition, the focus will be to analyze the risk of order financing from the perspective of banks and other financial institutions. Additionally, this paper will use the CreditRisk + model based on insurance actuarial principles to manage credit risk in order financing business based on foreign currency settlement, in conjunction with the characteristics of supply chain finance and multinational supply chain. Furthermore, a risk measurement method for the application of order financing in multinational supply chains will be provided. Ultimately, the experiments show that the solution of this paper defines and analyzes the financial risks brought by order financing business to bank financing.

Learning from History-A Risk Management Perspective

Though risk management and its application in the corporate world are new, its essence is very old. One must remember that risk is always about the future and the future is always unknown. There is no idea what will unfold in the future, however, some ideas about the future can be assessed based on past data, present information, and judicious judgment about the future. In the life insurance business which is about long-term assessment of risk is based on similar methodologies. Life insurance businesses have been successful throughout the world based on actuarial principles. To address any risk, it is very important to first identify the risk, assess its likely impact, and plan for preventative action now, to minimize the impact of the risk, should risk materializes. Risk assessment requires a mindset with a vision to anticipate the future based on certain key risk indicators of the present which always emanate important information about the expected future. In the very recent past we witnessed economic slowdown resulting from reduced economic activities, the key question that is addressed in this article is, could this have been anticipated to address the economic risks to take mitigating actions earlier than later

A Cyber-Insurance Scheme for Water Distribution Systems Considering Malicious Cyberattacks

As one of the national critical infrastructures, the water distribution system supports our daily life and economic growth, the failure of which may lead to catastrophic results. Besides the uncertainty from the system component failures, cyberattacks are vital to the secure system operation and have great impacts on the reliability of the water supply service. Malicious attackers may intrude into the supervisory control and data acquisition (SCADA) system of pump stations in the water distribution networks and interrupt the water supply to the customers. Cyber insurance is emerging as a promising financial tool in system risk management. In this paper, cyber insurance is proposed for the cyber risk management of the water distribution system. A semi-Markov process (SMP) model is devised to model the cyberattacks against pump stations in the water distribution system. Both the impacts of the independent cyber risks in the individual distribution network and the correlated cyber risks shared across different water distribution networks are evaluated and modeled. A sequential Monte Carlo Simulation (MCS) based algorithm is developed to evaluate the system loss. Cyber insurance premiums for the water distribution networks are designed based on the actuarial principles and potential system losses. Case studies are also performed on multiple representative water distribution networks, and the results demonstrate the validity of the proposed cyber insurance model.

Some actuarial mathematical models for insuring the susceptibles of a communicable disease

Using epidemiological and actuarial analysis, this paper formulates some new actuarial mathematical models, called S-I-DR-S models, for insuring the susceptibles of a population exposed to a communicable disease. Epidemiologically, the population is structured into four demographic groups, namely: susceptibles [Formula: see text], infectives [Formula: see text], diseased [Formula: see text] and recovered [Formula: see text], with the latter automatically re-entering the group of susceptibles [Formula: see text]. The insurance policies are targeted at the members of the susceptible group who face the risk of infection and death due to the disease. Using actuarial techniques and principles, we determine some interesting features of the model, namely, (a) financial obligations of the parties, (b) present value of premiums, (c) quantum of claims by infected policy holders (PHs), (d) quantum of claims on behalf of deceased PHs, (e) cumulative insurance reserve for annuity and (f) lump sum plan. To check the risk of insolvency, premium adjustment for the PHs is also considered.

Tristram Shandy in the Age of Insurance

AbstractIn 1762 the Equitable Life Assurance Society was founded, the first to calculate its premiums on actuarial principles. Its origin coincided with an increased appreciation of domestic risk and an expanding market for insurance products: the third quarter of the century saw a sharp spike in the issuing of fire insurance policies. In 1759 Sterne's Tristram Shandy introduced a character whose developmental years are almost uniquely beset by hazard and contingency. This article argues that Sterne's novel is constituted by an insurance ‘mentality’ in its appreciation of the inherent risks of life and how these might be calculated and mitigated.

THE BEGINNINGS OF MODERN COLLECTIVE OCCUPATIONAL PENSIONS IN BUSINESS IN SCANDINAVIA, CA. 1900–1930

The first three decades of the 20th century marked the beginning of modern collective occupational pensions for salaried business employees in the three Scandinavian countries. Pension premiums were derived from actuarial principles and pension entitlement was financially and legally secured. Relatively few salaried business employees were covered by these new occupational pension schemes until the 1930s. There were similar developments as well as different outcomes in the three countries. In their first three decades, the relative success of such schemes, and the participation of salaried employees in them, seems to have been largest in Denmark and lowest – as well as starting latest – in Norway. The development of occupational pensions in business is compared with Britain and Switzerland as well as with occupational pensions for public employees in the Scandinavian countries; the latter clearly functioning as a model. The new principles for occupational pensions in business, established during and after World War I, proved long lasting and increasingly important. In Norway, defined benefit pension schemes that started in business during World War I were not replaced by defined contribution pension schemes until after 2000.

A New Class of Probability Distortion Operators with an Application to CAT Bonds

The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the Wang (2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g., skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.

HT3 - Actuarial Approaches To Modelling and Mitigating Financial Uncertainty in Recommending New Drugs and Health Technologies

Health technology assessments (HTAs) are fundamental in informing decisions on reimbursement, assessing whether premium drug pricing is commensurate with the expected incremental health benefits. In collaboration with the National Institute for Health and Care Excellence (NICE) in England, alternative methodological approaches to the appraisals of new drugs and technologies are explored, which offer valuable perspectives on handling financial uncertainty. Building on the evidence from recent hepatitis C manufacturer submissions to NICE, a state-dependent Markov model is replicated as a proof of concept to demonstrate the degree of financial uncertainty around recommending new drugs for routine commissioning. A theoretical framework is developed to illustrate how risk sharing agreements focussing on parameters and assumptions with the greatest potential budget impact can be implemented. Selected risk mitigation strategies prevalent in insurance settings such as stop-loss schemes and risk corridors support the design of one-way and two-way risk sharing agreements. These are tailored to meet the specificities of the model assumptions from the case study. Recognising the strong influence of the mean incremental cost-effectiveness ratio (ICER) in decision-making, but also the lack of a defined framework for appraising uncertainty around this ratio, reimbursement decisions based on the median ICER and a 75% percentile ICER are explored in the simulation. A measure of variability such as the coefficient of variation supplements the proposed approaches, which incorporate financial uncertainty more explicitly due to the allocation of probability distributions to cost and outcome metrics. Finally, the methodology reinforces the need to monitor actual experience against projections through retrospective reviews of historical medical data, to inform the value of the recoverable per the risk sharing terms. It further builds on actuarial principles and stochastic modelling for handling the financial yet uncertain impact of recommending new drugs and health technologies in a context of value-based care.

DINÂMICA DEMOGRÁFICA, GESTÃO PÚBLICA E REGIMES PRÓPRIOS DE PREVIDÊNCIA SOCIAL: OPORTUNIDADES E DESAFIOS PARA OS SERVIDORES E MUNICIPIOS

The article aims to discuss the advantages and disadvantages in the creation of the Proper Social SecuritySystems (RPPS). Based on the analysis of regulatory, institutional and actuarial principles, we seek to assess theopportunities and challenges for public servers and municipalities. According to the results, we can conclude thatthe Ministry of Social Security has invested in actions that seek to reduce the pressure on the General SocialSecurity System (RGPS). However, without an individual assessment, the effort to universalize RPPS can resultin critical problems, especially for servers. On the other hand, considering the potential relief on RGPS, if allmunicipalities that do not yet have a RPPS solve create it, would reach only 2.1% of municipal servers in smallcities.

Towards Socially Responsible (Re)Insurance Underwriting Practices: Readily Available Big Dataa Contributions to Optimize Catastrophe Risk Management

Today's advances in big data technologies readily allow for storing large inter-dependent data sets of historical and modeled natural hazard and financial data and unifying their granularity and accuracy with common geo-spatial and risk-type record identifiers. This is a significant component at both single insurance account, and even more so at the larger multi-policy portfolio scale for enabling optimal and socially responsible insurance underwriting practices. This supports insurance risk transfers by creating more accurate and all-uncertainty encompassing pricing techniques, and exposes these techniques and methodologies to all market players, including insurance policy holders via transparent statistical and actuarial principles.

Pricing Flood Insurance: How and Why the NFIP Differs from a Private Insurance Company

Flood insurance in the United States is offered through the federal National Flood Insurance Program (NFIP). After going deeply into debt following the 2005 hurricane season, pricing in the program has been the subject of debate and two reform bills. Private sector insurance pricing has often been used as a benchmark in these discussions. In this paper, we explain NFIP pricing in the context of actuarial pricing principles, clarify why some polices are priced below what is considered to be the full risk rate, and explain how and, more importantly, why NFIP pricing practices differ from the private sector. NFIP pricing has incorporated other program goals that are at times at odds with the ability to cover all payouts for insured losses without taxpayer support. These multiple programmatic goals make the private sector a questionable analog for the NFIP.

A Risk-Based Approach to Wildland Fire Budgetary Planning

The financial impact of wildfire management within the USDA Forest Service challenges the ability of the agency to meet societal demands and maintain forest health. The extent of this financial crisis has been attributed to historical and continuing fire management practices, changing climatic conditions, and increasing human development in fire-prone areas, as well as the lack of financial accountability of fire managers and misaligned incentive structures. In this article, we focus on incentives related to cost containment. We review the literature on the incentive structure facing wildfire managers and describe how the incentive structure does not sufficiently reward cost containment. We then cover a range of possible approaches to promote cost containment, culminating in a novel solution premised on the application of actuarial principles to wildfire budgetary planning that we believe most closely aligns with the Forest Service's transition to risk-based management paradigms and that most comprehensively incentivizes containment across the spectrum of wildfire management activities. We illustrate through a proof of concept case study how risk-based performance measures would be calculated and compare our results with historic suppression expenditures. Preliminary results suggest that our simulation model performs well in a relative sense to identify high- and low-cost forests, and we detail modeling improvements to refine estimates. We then illustrate potential extension to an actuarial system, which would further incentivize appropriate risk management and cost containment across the fire management continuum. We address the strengths and weaknesses of the proposed approaches, including potential roadblocks to implementation, and conclude by summarizing our major findings and offer recommen- dations for future agency direction. FOR .S CI. 59(1):63-77.

TIME‐CONSISTENT AND MARKET‐CONSISTENT EVALUATIONS

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market‐consistent evaluation procedure which we call “two‐step market evaluation.” This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two‐step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time‐consistent and market‐consistent is a two‐step market evaluation. We also give characterization results and examples in terms of g‐expectations in a Brownian‐Poisson setting.

One-sided commitment in dynamic insurance contracts: Evidence from private health insurance in Germany

This paper studies long-term private health insurance (PHI) in Germany. It describes the main actuarial principles of premium calculation and relates these to existing theory. In the German PHI policyholders do not commit to renewing their insurance contracts, but insurers commit to offering renewal at a premium rate that does not reflect revealed future information about the insured risk. We show that empirical results are consistent with theoretical predictions from one-sided commitment models: front-loading in premiums generates a lock-in of consumers, and more front-loading is generally associated with lower lapzation. Due to a lack of consumer commitment, dynamic information revelation about risk type implies that high-risk policyholders are more likely to retain their PHI contracts than are low-risk types.

A Markov Chain Based No-Claim-Discount System

In automobile insurance, among other general insurance policies, it is quite common to reduce the premium by a factor in case the insured does not make any claim in a given period. This is popularly known as NCD or no-claim-discount. Equally popular is the practice of increasing (known as ‘loading’) the premium, in case a claim is made. In effect, either system amounts to a multi-layer premium policy, where any particular policyholder is required to pick the level depending on the history of claims (s)he made in the immediate past few years. In this study, we inspect the desirability of this multi-layer premium system (also referred to as NCD system); to start with we work with a given number of levels with fixed gaps, and eventually look to determine an appropriate number of levels, as well the optimum gaps between levels.The basic framework that we consider is that of a discrete time parameter Markov chain, where the state space consists of the different levels of the premium, and the state of a particular insured shifts randomly from an year to the next. The randomness of the transition is governed by the transition probability of causing an accident in a given year. We model this probability to be varying depending on quality of the driver. For the most part, we would be considering a finitely many groups of policyholders (drivers) characterized by respective probabilities of getting involved in an accident. The claim (damage) amount is assumed to have a known distribution, a log-normal one, for the sake of illustration. The parameters of this distribution need to be consistent with the basic premium level(s). We work under two possible behavior of all the policyholders. In the simpler version, we consider a driver would claim whenever (s)he incurs a damage from accident. In the second framework, (s)he would make a claim only if the (claim) damage amount exceeds the potential loss in the form of losing NCD. In making this judgment (s)he would need to take into account the effect of any more accident in the near future, and it is assumed that (s)he would rule out the such eventuality. This assumption is reasonable in the sense that, in reality, most drivers think very positively about their own driving ability; also, one is likely to be extra careful after getting involved in an accident.We obtain the stationary distribution for each group of policyholders. This reflects the distribution of a particular group over the various levels of premium in the long run. For example, one can obtain the percentage of ‘good’ drivers expected to receive the fully discounted rate in the long run. A comparative study of these stationary distributions over the various groups considered, form the basis of appropriateness of the assumed NCD system. We show the existence of a stationary distribution, irrespective of the possible differences in the various NCD systems.Finally, we look at the feasibility of evolving a NCD system which would be fair in the sense that the premium collected from any specific group would cover the expected claim amount from that group asymptotically. Use of simulation, properties of Markov chain, along with the basic actuarial and statistical principles form the core of the methodologies adopted for this study.

A note on utility based pricing and asymptotic risk diversification

In principle, liabilities combining both insurancial risks (e.g. mortality/longevity, crop yield,...) and pure financial risks cannot be priced neither by applying the usual actuarial principles of diversification, nor by arbitrage-free replication arguments. Still, it has been often proposed in the literature to combine these two approaches by suggesting to hedge a pure financial payoff computed by taking the mean under the historical/objective probability measure on the part of the risk that can be diversified. Not surprisingly, simple examples show that this approach is typically inconsistent for risk adverse agents. We show that it can nevertheless be recovered asymptotically if we consider a sequence of agents whose absolute risk aversions go to zero and if the number of sold claims goes to infinity simultaneously. This follows from a general convergence result on utility indifference prices which is valid for both complete and incomplete financial markets. In particular, if the underlying financial market is complete, the limit price corresponds to the hedging cost of the mean payoff. If the financial market is incomplete but the agents behave asymptotically as exponential utility maximizers with vanishing risk aversion, we show that the utility indifference price converges to the expectation of the discounted payoff under the minimal entropy martingale measure.

Time-Consistent and Market-Consistent Evaluations

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with a continuous stock prices process every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

Time-Consistent and Market-Consistent Evaluations

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with a continuous stock prices process every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.