Fair Premium Research Articles

Individual’s Choice on Buying Life Insurance Products in Nepal

This study examines the factors influencing individual’s choice on buying life insurance products in Nepal. An individual’s choice on buying life insurance policy is selected as the dependent variable. The independent variables are company loyalty, premium charge, agent, claim settlement and company image. The primary source of data is used to assess the opinions of the respondents regarding individual’s choice on buying insurance products in Nepal. The study is based on primary data with 151 respondents. To achieve the purpose of the study, structured questionnaires is prepared. The correlation coefficients and regression models are estimated to test the significance and importance of different factors driving individual’s choice on buying life insurance products in Nepal. The study showed that company loyalty has a positive impact on individual’s choice on buying life insurance policy. It indicates that company’s loyalty towards consumer stimulates the individual’s choice on buying insurance products in Nepal. Similarly, premium charge has a positive impact on individual’s choice on buying life insurance products. It indicates that fair premium charge stimulates the individual choice. Similarly, agent of the respective company has a positive impact on individual’s choice on buying life insurance products. It indicates that the behaviour and knowledge of agents impulse individuals’ choice on buying life insurance products. The study also showed that claim settlement has a positive impact on individual’s choice. It indicates that proper claim settlement process stimulates the individuals’ choice on buying life insurance products. Furthermore, company image has a positive impact on individual’s choice on buying life insurance policy. It indicates that good company image stimulates individual’s choice on buying life insurance products in Nepal.

Unveiling Mispricing Risks: Nonlarge Homogeneous Portfolio Factor Copula Models for Enhanced Valuation of Subordinated Loan Securitization

AbstractThis paper presents an innovative factor copula model for collateralized loan obligation (CLO) tranche valuation, incorporating non‐Gaussian distributions and dynamic correlations without relying on the large homogeneous portfolio (LHP) assumption. Through numerical analyses and comparisons with LHP models, I find that non‐LHP models produce higher tranche spreads, especially for lower‐rated tranches. Sensitivity analysis reveals varying sensitivities to changes in the number of collaterals, risk‐free rate, average collateral ratings, recovery rates, and time to maturity. The non‐LHP one‐factor copula models, including stochastic correlation and random factor loading models, outperform LHP models in root mean squared errors when calibrated to market data. The results underscore the importance of considering model limitations in CLO tranche pricing and highlight potential mispricing of spread risk in higher‐rated tranches using LHP models. The proposed models contribute to a more comprehensive understanding of CLO tranche pricing by accounting for various factors and assumptions influencing fair premiums.

On bayesian bonus-malus premium under linex loss function with applications

The majority of bonus-malus systems (BMS) determine the premium for each policyholder solely based on their claim frequency. Adopting this method would be unjust. A driver who files a claim for small damage cannot be subjected to the same penalties as a driver responsible for a claim involving significant damage. To achieve a balance in the portfolio between good and bad drivers, a new portion of the premium is computed as a compromise. To do this, the claim severity is created and assessed to provide a fair premium. The consideration was determined by taking into account both the quantity and magnitude of the claims. This work assumes that the frequency of claims follows a Poisson-Akash distribution, but the severity of claims follows a newly proposed distribution known as the Inverse-Gamma Lindley distribution. The bonus-malus premiums were computed using the Bayesian approach for both the frequency and severity of claims. The premium is computed using the asymmetric Linex loss function for both the frequency and severity of claims in the bonus-malus system. Illustrative instances utilizing an actual dataset for the application of BMS are presented, showcasing the use of claim frequency alone and the combination of claim frequency and claim severity. The R software is employed for these demonstrations. We concluded this paper with a discussion comparing the premiums obtained in each case.

Facilitators and Barriers of Incremental Innovation by Fixed Dose Combinations in Cardiovascular Diseases.

Despite the availability of affordable pharmaceuticals treating cardiovascular diseases (CVDs), many of the risk factors remain poorly controlled. Fixed-dose combinations (FDCs), a form of incremental innovation, have already demonstrated improvements over combinations of single medicines in adherence and hard clinical endpoints. Nevertheless, there are many barriers related to the wider use of FDCs in CVDs. Our aim was to identify these barriers and explore system-level facilitators from a multi-stakeholder perspective. Identified barriers include (i) hurdles in evidence generation for manufacturers, (ii) limited acceptance of adherence as an endpoint by clinical guideline developers and policymakers, (iii) limited options for a price premium for incremental innovation for healthcare payers, (iv) limited availability of real-world evidence, and (v) methodological issues to measure improved adherence. Initiatives to standardize and link healthcare databases in European countries, movements towards improved patient centricity in healthcare, and extended value assessment provide opportunities to capture the benefits of FDCs. Still, there is an emerging need to facilitate the generalizability of sporadic clinical evidence across different FDCs and to improve adherence measures. Finally, healthcare payers need to be convinced to pay a fair premium price for the added value of FDCs to incentivize incremental innovation in CVD treatment.

A Robust Numerical Simulation of a Fractional Black–Scholes Equation for Pricing American Options

After the discovery of fractal structures of financial markets, fractional partial differential equations (fPDEs) became very popular in studying dynamics of financial markets. Available research results involves two key modelling aspects; firstly, derivation of tractable asset pricing models, those that closely reflects the actual dynamics of financial markets. Secondly, the development of robust numerical solution methods. Often times, most the effective models are of a nonlinear nature, and as such, reliable analytical solution methods are seldomly available. On the other hand, the accurate value of American options strongly lies on the unknown free boundaries associated with these types of derivative contracts. The free boundaries emanates from the flexibility of the early exercise features with American options. To the best of our knowledge, the approach of pricing American options under the fractional calculus framework has not been extensively explored in literature, and an obvious wider research gap still exist on the design of robust solution methods for pricing American option problems formulated under the fractional calculus framework. Therefore, this paper serve to propose a robust numerical scheme for solving time-fractional Black–Scholes PDEs for pricing American put option problems. The proposed scheme is based on the front-fixing algorithm, under which the early exercise boundaries are transformed into fixed boundaries, allowing for a simultaneous computation of optimal exercise boundaries and their corresponding fair premiums. Results herein indicate that, the proposed numerical scheme is consistent, stable, convergent with order O(h2,k)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(h^2,k)$$\\end{document}, and also does guarantee positivity of solutions under all possible market conditions.

On duration effects in non-life insurance pricing

The paper discusses duration effects on the consistency of mean parameter and dispersion parameter estimators in exponential dispersion families (EDFs) that are the standard models used for non-life insurance pricing. Focus is on the standard generalised linear model assumptions where both the mean and variance, conditional on duration, are linear functions in terms of duration. We derive simple convergence results that highlight consequences when the linear conditional moment assumptions are not satisfied. These results illustrate that: (i) the resulting mean estimators always have a relevant asymptotic interpretation in terms of the duration adjusted actuarially fair premium—a premium that only agrees with the standard actuarial premium using a duration equal to one, given that the expected value is linear in the duration; (ii) deviance based estimators of the dispersion parameter in an EDF should be avoided in favour of Pearson estimators; (iii) unless the linear moment assumptions are satisfied, consistency of dispersion and plug-in variance estimators can not be guaranteed and may result in spurious over-dispersion. The results provide explicit conditions on the underlying data generating process that will lead to spurious over-dispersion that can be used for model checking. This is illustrated based on real insurance data, where it is concluded that the linear moment assumptions are violated, which results in non-negligible spurious over-dispersion.

On Correlation Aversion and Insurance Demand

This is a study of decision problems under two-dimensional risk. We use an existing index of absolute correlation aversion to conveniently classify bivariate preferences, with respect to attitudes toward this risk. This classification seems to be more important than whether decision makers are correlation-averse or correlation-seeking for the study of insurance demand when a loss has a multidimensional impact. On this note, we also re-examine Mossin’s theorem under bivariate preferences, where full insurance is preferred with a fair premium, while less than full coverage is preferred with a proportional premium loading. Furthermore, based on the comparative statics of this two-dimensional insurance model for changes in correlation aversion, we derive testable implications about the classification of bivariate utility functions. For the particular case when the two-dimensional risk can be interpreted as risk on income and health, we identify the form of separable utility functions depending on health status and income that is consistent with household disability insurance decisions.

Epidemic modelling and actuarial applications for pandemic insurance: a case study of Victoria, Australia

Abstract With the recent outbreak of COVID-19, evaluating the epidemic risk appears to be a pressing issue of global concern and one of the major challenges recently. In the fight against pandemics, the ability to understand, model, and forecast the transmission dynamics of infectious diseases plays a crucial role. This paper provides an overview of foundational compartment models and introduces the Susceptible-Exposed-Infected-Containing-3-Substates-Recovered-Dead model to study the dynamics of COVID-19. A meticulous data calibration procedure is employed to study the evolution trend of an actual pandemic using real-world data from Victoria, Australia. Additionally, the paper discusses innovative applications of epidemic models to the insurance industry, which are currently under investigation. Through the use of the newly developed analytically tractable model, insurance companies are able to determine fair premium levels during an outbreak. Moreover, the paper provides practical guidance for insurance companies by examining the variation in reserve levels over time.

Compound Poisson–Lindley process with Sarmanov dependence structure and its application for premium-based spectral risk forecasting

One of the fundamental challenges insurance companies face is forecasting a fair premium that covers the cost of claims while maintaining profitability. To comprehend the risk of insurance claims, one needs to construct a collective risk model. In this study, we aim to propose a new collective risk model, namely a dependent compound Poisson–Lindley process. We capture the dependence structure between the claim frequency and severity using a bivariate Sarmanov distribution. We then employ this model to perform premium-based risk measure forecasting such that the insurance company can obtain the premium value for the policyholder. We accomplish this task by proposing a specific risk spectrum to adjust the premium for risk-aversion-type insurance companies. Our main results demonstrate that a collective risk model based on the Poisson–Lindley process is able to capture the overdispersion phenomenon in claim frequency that is common in practice. This ability is confirmed by our simulation conducted using real insurance data. Furthermore, when accounting for the Sarmanov dependence structure, the resulting premium value becomes more appropriate.

The Impact of Health Risks on Individual Decision Making: Focusing on the Demand for Insurance and Risky Assets

This study examines the impact of health and health risks on individuals' decision-making using a bivariate utility function, where the level of utility depends on both wealth and health. The findings are as follows, first, partial insurance may be optimal even under an actuarially fair insurance premium. Conversely, full insurance or over insurance may be optimal, even under an actuarially unfavorable premium. Second, when the utility function exhibits cross-risk vulnerability toward health, the presence of unfair health risks, independent of losses, increases the demand for insurance. Third, correlation-loving individuals reduce their investment in risky assets as health deteriorates when their preference exhibits decreasing absolute risk aversion (DARA) in wealth and absolute risk aversion (ARA) in wealth is sufficiently large. Conversely, correlation-averse individuals reduce their investment in risky assets as health deteriorates when their preference for DARA and ARA in wealth is sufficiently small. Fourth, when the utility function exhibits cross-risk vulnerability toward health, the presence of unfair health risks independent of the returns of risky assets reduces the demand for those assets.

Privacy Protection, At What Cost? Exploring the Regulatory Resistance to Data Technology in Auto Insurance

AbstractRegulatory and sociological resistance to new market-driven technologies, particularly to those that rely on collection and analysis of personal data, is prevalent even in cases where the technology creates large social value and saves lives. This article is a case study of such tragic technology resistance, focusing on tracking devices in cars which allow auto insurers to monitor how policyholders drive and adjust the premiums accordingly. Growing empirical work reveals that such “usage-based insurance” induces safer driving, reducing fatal accidents by almost one third, and resulting in more affordable and fair premiums. Yet, California prohibits this technology and other states limit its effectiveness, largely in the interest of privacy protection. The article evaluates the justifications fueling the restrictive regulation vis-à-vis the loss of lives resulting from this regulation. It concludes that the social benefits of the tracking technology dramatically outweigh the privacy and related costs.

Remote Sensing Application in Pure Premium Rate-Making of Winter Wheat Crop Insurance

Crop insurance is a crucial way to avoid disaster losses and to guarantee farmers’ basic production income in China and abroad. Securing agricultural production is a critical way to eradicate hunger and reduce poverty and an essential means to achieve the UN Sustainable Development Goals. How to pay out more quickly and fairly after a disaster has become an urgent issue for agricultural insurance. The standard domestic crop insurance rate is determined based on the statistical data of the entire administrative unit and ignores the spatial risk difference of disasters inside the administrative unit. Therefore, obtaining a pure premium based on crops inside the administrative unit is a key problem. Based on remote sensing data and insurance actuarial models, we studied and determined the fair premium rates to insure winter wheat at the farmer level in Heze, Shandong, China. Our study shows that remote sensing data can provide data security for determining a pure premium rate at the level of individual farms, and provide the primary reference for determining farmer-level crop insurance premium rates. The use of remote sensing for determining those rates can improve the customization of crop insurance and reduce farmers’ lower incomes due to exposure to natural disasters, improve farmers’ resilience to risk, and prevent a return to poverty due to disasters, ultimately reaching the UN Sustainable Development goals of eradicating hunger and reducing poverty.

PENENTUAN NILAI PREMI ASURANSI PERTANIAN BERBASIS HARGA INTERNASIONAL MENGGUNAKAN MODEL MEAN REVERSION DENGAN MUSIMAN

The seasonal cycle causes cocoa price movements in the international market to fluctuate. This certainly affects the development of cocoa prices at the producer level, causing uncertainty about the prices received by farmers. International price-based agricultural insurance is an alternative to protect farmers against global price fluctuations. Compensation is given if the global price of cocoa falls below the agreed trigger value. This study aims to calculate the fair premium value for agricultural insurance based on international prices for cocoa in the Tabanan Regency, Bali, which was simulated using a mean reversion model with seasonality. To perform the simulation, the first step is to estimate the parameters of the seasonal model and the mean reversion model. Next, simulate the international price of cocoa. Then, determine the trigger value based on the percentile of the simulation data. Finally, calculate the premium value using the cash-or-nothing put option with the Black-Scholes model. The results show that the premium value which is considered fair lies between 5,77% to 11,08% of the insured value.

Prospects for weather-indexed insurance for blueberry growers

PurposeThe authors investigate whether an index-based weather insurance (WII) product can complement or replace existing traditional crop yield insurance for mitigating farmers' financial risks, with an application to blueberry growers in British Columbia (BC).Design/methodology/approachA hybrid model combining expected utility (EU) and prospect values is developed to analyse farmers' demand for WII.FindingsWhile weather data are used to investigate supply elements, a hybrid model combining EU theory and prospect theory (PT) is developed to analyse farmers' demand for WII. On the supply side, a quality index is constructed and the relationship between the quality index and key weather parameters is quantified using a partial least squares structural model. The authors then model weather parameters via time-series analysis and statistical distributions to provide reasonable estimates for calculating actuarially sound insurance premiums for a rainfall indexed, insurance product. This model indicates that decreases in the proportion of a blueberry grower's total revenue and revenue volatility will decrease the possibility that they participate in WII. At the same time, an increase in the value loss aversion coefficient and WII's basis risk further leads to less demand for WII. In short, a grower may decide not to participate in WII at an actuarially fair premium due to the combined effects of the above factors. Overall, while the supply analysis enables us to demonstrate that WII can potentially help in mitigating farmers' financial risks, it turns out that, on the demand side, blueberry growers are unwilling to pay for such a product without large government subsidies.Originality/valueThe authors argue that the demand for insurance may be affected by the level and the volatility of a berry grower's total revenue. Hence, the authors propose a hybrid expression that assumes a farmer seeks to maximize the total utility function to capture the rational and intuitive parts of a farmer's decision-making process. The EU represents rationality and the prospect value represents the intuitive component. Meanwhile, the authors investigate the possibility of using key weather parameters to construct a berry quality index – one that could be applied to other agricultural areas for studying the relationship between weather conditions and product quality.

Bonus-Malus Premiums Based on Claim Frequency and the Size of Claims

The bonus-malus system (BMS) is one of the most widely used tools in merit-rating automobile insurance, with the primary goal of ensuring that fair premiums are paid by all policyholders. The traditional BMS is dependent only on the claim frequency. Thus, an insured person who makes a claim with a small severity is penalized unfairly compared to an individual who makes a large severity claim. This study proposes a model for estimating the bonus-malus premium by employing a limit value (monetary unit) which distinguishes claim size into small and large based on claim frequency and claim severity distributions. This assists in determining the penalties for policyholders with claim sizes falling above and below the limit value. The number of claims is assumed to follow a Poisson distribution, and the total number of claims with a size greater than the limit value is considered a binomial distribution. The underlying risk of each policyholder is assumed to follow a beta Lindley distribution and is referred to as the prior distribution. Each policyholder’s claim size is also assumed to follow a gamma distribution, with the Lindley distribution considered as the prior distribution. Bonus-malus premiums are calculated following the Bayesian method. Practical examples using an actual data set are provided, and the results generated are compared to those produced using the traditional Poisson binomial-exponential beta model. This methodology provides a more equitable mechanism for penalizing policyholders in the portfolio.

Why not insure prices? Experimental evidence from Peru

In a competitive market, a profit-maximizing producer's total revenue is determined both by the quantity of output she chooses to produce and by the price at which she can sell that output. Of these two variables, only output is in part or wholly within the producer's control, price being entirely determined by market forces. Given that, it is puzzling that the literature studying the effects of providing insurance to producers in low- and middle-income countries has ignored price risk entirely, focusing instead on insuring output. We run an artefactual lab-in-the-field experiment in Peru to look at the effects of insurance against output price risk on production. We randomize the order of three games: (i) a baseline game in which price risk is introduced at random, (ii) the baseline game to which we add mandatory insurance against price risk sold at an actuarially fair premium, and (iii) the baseline game to which we add voluntary insurance against price risk sold at the actuarially fair premium, but for which we offer a random 0-, 50- or 100% discount to exogenize take-up. Our results show that, on average, (i) price risk does not significantly change production relative to price certainty and (ii) neither does the provision of compulsory insurance against price risk, but the introduction of voluntary price risk (iii) causes the average producer on the market to produce more in situations of price risk than in situations of price certainty, and (iv) causes the average producer on the market to produce more in situations of price certainty than in cases where there is no insurance or where insurance is mandatory. When looking only at situations where there is price risk, (v) this is due almost entirely to the insurance rather than to selection into purchasing the insurance. Our findings further suggest that (vi) even in the absence of the discount, the insurance against price risk would have a large (i.e., 70%) take-up rate.

Can 7000 Years of flood history inform actual flood risk management? A case study on Lake Mondsee, Austria

Flood risk models typically rely on discharge records of time series no longer than a few hundred years, which leads to high uncertainty in the estimates for major flood events. In this paper, we investigate the capability of geological flood records retrieved from lake sediment cores to prolong available data sets, lower the uncertainty of flood risk analysis, and detect changes in flood patterns by releasing the common assumption of stationarity. Paleoflood records of Lake Mondsee, Austria, covering 7000 years are linked to flood damage data of the considered catchment area to calculate (1) the average annual damage, i.e. the fair premium and (2) the damage at 99.5% Value at Risk, i.e. the Solvency II capital requirement. To illustrate our results, the performance of a hypothetical catastrophe fund for these 7000 years is studied at current vulnerability levels. Our findings show that high resolution paleoflood records with robust chronologies and flood information have significant impacts on flood model outcomes for disaster risk management and that damage potentials derived merely from recent damage data may overestimate actual risks.

Stackelberg differential game for insurance under model ambiguity

We study a dynamic Stackelberg differential game between a buyer and a seller of insurance policies in a spectrally negative Lévy framework, in which both parties are ambiguous about the intensity and severity of insurable losses. Both the buyer and seller aim to maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a quadratic penalty for ambiguity, we obtain the equilibrium in closed form. Our main results show that the buyer's robust optimal indemnity is a coinsurance with proportion less than one-half, which increases (resp. decreases) as the buyer (resp. seller) becomes more ambiguity averse. Also we show that the seller's robust optimal premium rule equals the net premium under the buyer's optimally distorted probability, which is the buyer's “best hope,” and it exceeds the actuarially fair premium under the seller's optimally distorted probability measure so is, thereby, acceptable to the seller.

Market insurance and endogenous saving with multiple loss states

The standard one-period model for insurance demand does not consider the interaction between the present and the future. Reflecting this observation, we analyze intertemporal insurance demand and saving in a two-period model with multiple loss states. When an individual has no access to a capital market, we first find that an actuarially fair premium does not guarantee full insurance in general, unlike in the standard approach. Income stream and discount factors are also important in determining insurance demand. Second, insurance is neither an inferior good nor a Giffen good. Third, an increase in concavity of the utility function does not always lead to an increase in insurance demand. The current income level and changes in downside risk aversion affect insurance demand. When the individual has access to a capital market, we further have the following observations. Fourth, an actuarially fair premium leads to full insurance. Fifth, insurance is an inferior good and can be a Giffen good under decreasing absolute risk aversion (DARA). An increase in the interest rate leads to a lower insurance demand and a higher saving when the relative risk aversion is less than unity. Lastly, an increase in concavity of the utility function leads to an increase in insurance demand and a decrease in saving. In conjunction, our findings point to the fact that the standard results are not obtainable if insurance demand is considered in isolation from the capital market.

Temperature effects on crop yields in heat index insurance

Heat can cause substantial yield losses in crop production and climate change is increasing the risk of this kind of damage. Weather index insurance can help to reduce the financial losses resulting from heat exposure. This paper introduces crop-specific payout functions based on restricted cubic splines in heat index insurance. The use of restricted cubic splines is a cutting-edge method to reflect empirically estimated temperature effects on crop yields and to estimate temperature-related yield losses. The integration of these temperature effects in payout functions facilitates insurance design and allows hourly temperatures to be used as the underlying index. An empirical analysis is used to assess heat stress effects for a panel of East German winter wheat and winter rapeseed producers, to calibrate insurance contracts accordingly and simulate the resulting risk reducing capacities. We find that the insurance scheme introduced here leads to statistically and economically significant out-of-sample risk reducing capacities for farmers, i.e. risk premiums are reduced by up to approximately 20% at the median, in comparison to the uninsured status and at the actuarially fair premium. Moreover, we highlight that policy-makers can support the cost-efficient provision of market-based weather index insurance by fostering data collection and data provision.