This paper examines an insurer’s optimal asset allocation and reinsurance policies. The financial market framework includes one risk-free and one risky asset. The insurer has two business lines, where the ordinary claim process is modeled by a compound Poisson process and catastrophic claims follow a compound dynamic contagion process. The dynamic contagion process, which is a generalization of the externally exciting Cox process with shot-noise intensity and the self-exciting Hawkes process, is enhanced by accommodating the dependency structure between the magnitude of contribution to intensity after initial events for catastrophic insurance products and its claim/loss size. We also consider the dependency structure between the positive effect on the intensity and the negative crashes on the risky financial asset when initial events occur. Our objective is to maximize the insurer’s expected utility of terminal surplus. We construct the extended Hamilton–Jacobi–Bellman (HJB) equation using dynamic programming principles to derive an explicit optimal reinsurance policy for ordinary claims. We further develop an iterative scheme for solving the value function and the optimal asset allocation policy and the reinsurance policy for catastrophic claims numerically, providing a rigorous convergence proof. Finally, we present numerical examples to demonstrate the impact of key parameters.

In this paper, we investigate asymmetric Nash bargaining in the context of proportional insurance contracts between a risk-averse insured and a risk-averse insurer, both seeking to enhance their expected utilities. We obtain a necessary and sufficient condition for the Pareto optimality of the status quo and derive the optimal Nash bargaining solution when the status quo is Pareto dominated. If the insured’s and the insurer’s risk preference exhibit decreasing absolute risk aversion and the insurer’s initial wealth decreases in the insurable risk in the sense of reversed hazard rate order, we show that both the optimal insurance coverage and the optimal insurance premium increase with the insured’s degree of risk aversion and the insurer’s bargaining power. If the insured’s risk preference further follows constant absolute risk aversion, we find that greater insurance coverage is induced as the insurer’s constant initial wealth increases.

In this paper, we study a two-period optimal insurance problem for a policyholder with mean-variance preferences who purchases proportional insurance at the beginning of each period. The insurance premium is calculated by a variance premium principle with a risk loading that depends on the policyholder’s claim history. We derive the time-consistent optimal insurance strategy in closed form and the optimal constant precommitment strategy in semiclosed form. For the optimal general precommitment strategy, we obtain the solution for the second period semi-explicitly and, then, the solution for the first period numerically via an efficient algorithm. Furthermore, we compare the three types of optimal strategies, highlighting their differences, and we examine the impact of the key model parameters on the optimal strategies and value functions.

The bonus-malus system (BMS) is a widely recognized and commonly employed risk management tool. A well-designed BMS can match expected insurance payments with estimated claims even in a diverse group of risks. Although there has been abundant research on improving bonus-malus (BM) systems, one important aspect has been overlooked: the stationary probability of a BMS satisfies the monotone likelihood ratio property. The monotone likelihood ratio for stationary probabilities allows us to better understand how riskier policyholders are more likely to remain in higher premium categories, while less risky policyholders are more likely to move toward lower premiums. This study establishes this property for BMSs that are described by an ergodic Markov chain with one possible claim and a transition rule +1/-d. We derive this result from the linear recurrences that characterize the stationary distribution; this represents a novel analytical approach in this domain. We also illustrate the practical implications of our findings: in the BM design problem, the premium scale is automatically monotonic.

An increasing number of disaster relief programs rely on weather data to trigger automated payouts. However, several factors can meaningfully affect payouts, including the choice of data set, its spatial resolution, and the historical reference period used to determine abnormal conditions to be indemnified. We investigate these issues for a subsidized rainfall-based insurance program in the U.S. using data averaged over 0.25° × 0.25° grids to trigger payouts. We simulate the program using 5x finer spatial resolution precipitation estimates and evaluate differences in payouts from the current design. Our analysis across the highest enrolling state (Texas) from 2012 to 2023 reveals that payout determinations would differ in 13% of cases, with payout amounts ranging from 46 to 83% of those calculated using the original data. This potentially reduces payouts by tens of millions annually, assuming unchanged premiums. We then discuss likely factors contributing to payout differences, including intra-grid variation, reference periods used, and varying precipitation distributions. Finally, to address basis risk concerns, we propose ways to use these results to identify where mismatches may lurk, in turn informing strategic sampling campaigns or alternative designs that could enhance the value of insurance and protect producers from downside risks of poor weather conditions.

The standard analytical framework of insurance markets by Einav and Finkelstein (EF) focuses on the problem of welfare loss for low-risk individuals. A key assumption of this framework is that demand and cost curves are tightly linked, meaning that people are willing to pay a price equal to their expected cost plus a risk premium. Using data from the German risk-adjustment system we show that the distribution of expected health care costs is extremely skewed. We show that incorporating the extreme skewness of predictable individual health care expenses in the EF framework has important welfare consequences, which are typically overlooked when using this framework for analysing the negative welfare effects of voluntary health insurance markets with asymmetric information. Rather than the welfare loss of low-risk individuals due to underinsurance, the main problem of voluntary health insurance markets is the welfare loss of high-risk individuals not getting access to health insurance and affordable health care. We discuss that among the policy approaches to reduce this problem, mandatory health insurance with mandatory cross subsidies is likely to be the most effective, which is typically not recognised when focusing primarily on the welfare loss for low-risk individuals.

This paper develops a theoretical framework to examine the technology adoption decisions of insurers and their impact on market share, considering heterogeneous customers and two representative insurers. Intuitively, when technology accessibility is observable, an insurer’s access to a new technology increases its market share, no matter whether it adopts the technology or not. However, when technology accessibility is unobservable, the insurer’s access to the new technology has additional side effects on its market share. First, the insurer may apply the available technology even if it increases costs and premiums, thereby decreasing market share. Second, the unobservable technology accessibility leads customers to expect that all insurers might have access to the new technology and underestimate the premium of those without access. This also decreases the market share of an insurer with access to the new technology. Our findings help explain the unclear relationship between technology adoption and the market share of insurance companies in practice.

Longevity risk is threatening the sustainability of traditional pension systems. To deal with this issue, decumulation strategies alternative to annuities have been proposed in the literature. However, heterogeneity in mortality experiences in the pool of policyholders due to socio-economic classes generates inequity, because of implicit wealth transfers from the more disadvantaged to the wealthier classes. We address this issue in a Group Self-Annuitization (GSA) scheme in the presence of stochastic mortality by proposing a redistributive GSA scheme where benefits are optimally shared across classes. The expected present values of the benefits in a standard GSA scheme show relevant gaps across socio-economic groups, which are reduced in the redistributive GSA scheme. We explore sensitivity to pool size, interest rates and mortality assumptions.

This paper investigates a well-known downside protection strategy called the constant proportion portfolio insurance (CPPI) in defined contribution (DC) pension fund modeling. Under discrete time trading CPPI, an investor faces the risk of portfolio value hitting the floor which denotes the process of guaranteed portfolio values. In this paper, we question how to deal with so-called ‘gap risk’ which may appear due to uncontrollable events resulting in a sudden drop in the market. In the market model considered, the risky asset price and the labor income are assumed to be continuous-time stochastic processes, whereas trading is restricted to discrete-time. In this setting, an exotic option (namely, the ‘cushion option’) is proposed with the aim of reducing the risk that the portfolio value falls below the defined floor. We analyze the effectiveness of the proposed exotic option for a DC plan CPPI strategy through Monte Carlo simulations and sensitivity analyses with respect to the parameters reflecting different setups.

The conditional expectation $m_{X}(s)=\mathrm{E}[X|S=s]$, where X and Y are two independent random variables with $S=X+Y$, plays a key role in various actuarial applications. For instance, considering the conditional mean risk-sharing rule, $m_X(s)$ determines the contribution of the agent holding the risk X to a risk-sharing pool. It is also a relevant function in the context of risk management, for example, when considering natural capital allocation principles. The monotonicity of $m_X(\!\cdot\!)$ is particularly significant under these frameworks, and it has been linked to log-concave densities since Efron (1965). However, the log-concavity assumption may not be realistic in some applications because it excludes heavy-tailed distributions. We consider random variables with regularly varying densities to illustrate how heavy tails can lead to a nonmonotonic behavior for $m_X(\!\cdot\!)$. This paper first aims to identify situations where $m_X(\!\cdot\!)$ could fail to be increasing according to the tail heaviness of X and Y. Second, the paper aims to study the asymptotic behavior of $m_X(s)$ as the value s of the sum gets large. The analysis is then extended to zero-augmented probability distributions, commonly encountered in applications to insurance, and to sums of more than two random variables and to two random variables with a Farlie–Gumbel–Morgenstern copula. Consequences for risk sharing and capital allocation are discussed. Many numerical examples illustrate the results.

Conditional risk measures and their associated risk contribution measures are commonly employed in finance and actuarial science for evaluating systemic risk and quantifying the effects of risk interactions. This paper introduces various types of contribution ratio measures based on the multivariate conditional value-at-risk (MCoVaR), multivariate conditional expected shortfall (MCoES), and multivariate marginal mean excess (MMME) studied in [34] (Ortega-Jiménez, P., Sordo, M., & Suárez-Llorens, A. (2021). Stochastic orders and multivariate measures of risk contagion. Insurance: Mathematics and Economics, vol. 96, 199–207) and [11] (Das, B., & Fasen-Hartmann, V. (2018). Risk contagion under regular variation and asymptotic tail independence. Journal of Multivariate Analysis 165(1), 194–215) to assess the relative effects of a single risk when other risks in a group are in distress. The properties of these contribution risk measures are examined, and sufficient conditions for comparing these measures between two sets of random vectors are established using univariate and multivariate stochastic orders and statistically dependent notions. Numerical examples are presented to validate these conditions. Finally, a real dataset from the cryptocurrency market is used to analyze the spillover effects through our proposed contribution measures.

We use recent advances in polynomial diffusion processes to develop a continuous-time joint mortality model for the actuarial valuation and risk analysis of life insurance liabilities. The model considers the stochastic nature of future mortality improvements and introduces a common subordinator for the marginal survival processes, resulting in a nontrivial dependence structure between the survival of pairs of individuals. Polynomial diffusion processes can be used to derive closed-form formulae for standard actuarial quantities. The model fits well with a classic dataset provided by a Canadian insurer and can be used to evaluate products issued to multiple lives, as shown through numerical applications.

We analyse the effect of natural catastrophes on insurance demand in a developing economy and the role of insurance regulation in this relationship. The analysis is based on a theoretical model and a panel regression using data for Vietnam. What makes Vietnam especially interesting is the fact that it is strongly affected by natural catastrophes and experienced a change in insurance regulation in recent years. The theoretical results indicate that a loss experience likely has a less positive effect on demand in developing economies than in developed economies. A higher insurance penetration and a tighter insurance regulation, however, can make the impact of a loss event more positive. These findings are mirrored by our empirical analysis: overall natural catastrophes decrease insurance demand of affected households in Vietnam. The enhancement of regulation was not only accompanied by increased insurance demand but it also reverses the effect of natural catastrophes on demand.

In this paper, we present experimental evidence on the effect adverse selection has on coverage choices and pricing in corporate insurance markets. Two sets of experimental data, each generated by experiments utilizing a specific parameterization of a corporate insurance decision, are presented to gauge these effects. In the first, subject behavior conforms to a unique equilibrium in which high risk firms choose higher coverage and contracts are priced accordingly. Insurers act competitively and convergence to equilibrium behavior is marked. In the second set, there is little evidence that subject behavior is consistent with either of the two equilibrium outcomes supported by the experimental setting—pooling by fully insuring losses and pooling by self insuring.

The tonuity, proposed by Chen et al. ((2019) ASTIN Bulletin: The Journal of the IAA, 49(1), 530.), is a combination of an immediate tontine and a deferred annuity. However, its switching time from tontine to annuity is fixed at the moment the contract is closed, possibly becoming sub-optimal if mortality changes over time. This article introduces an alternative tonuity product, wherein a dynamic switching condition is pivotal, relying on the observable mortality trends within a reference population. The switching from tontine to annuity then occurs automatically once the condition is satisfied. Using data from the Human Mortality Database and UK Continuous Mortality Investigation, we demonstrate that, in a changing environment, where an unforeseen mortality or longevity shock leads to an unexpected increase or decrease in mortality rates, the proposed dynamic tonuity contract can be preferable to the regular tonuity contract.

The association between economic variables and the frequency and duration of disability income insurance (DII) claims is well established. Across many jurisdictions, heightened levels of unemployment have been associated with both a higher incidence and a longer duration of DII claims. This motivated us to derive an asset portfolio for which the total asset value moves in line with the level of unemployment, thus, providing a natural match for the DII portfolio liabilities. To achieve this, we develop an economic tracking portfolio where the asset weights in the portfolio are chosen so that the portfolio value changes in a way that reflects, as closely as possible, the level of unemployment. To the best of our knowledge, this is the first paper applying economic tracking portfolios to hedge economic risk in DII. The methodology put forward to establish this asset-liability matching portfolio is illustrated using DII data from the UK between 2004 and 2016. The benefits of our approach for claims reserving in DII portfolios are illustrated using a simulation study.

The emergence of COVID-19 has resulted in a notable rise in mortality rates, consequently affecting various sectors, including the insurance industry. This paper analyzes the reflections of a sudden increase in mortality rates on the financial performance of a survival benefit scenario under the International Financial Reporting Standard 17. For this purpose, we thoroughly examined a single insurance scenario under four different states by modifying the interest and jump elements. We use Poisson-log bilinear Lee–Carter and Vasicek models for mortality and stochastic interest rate, respectively. Integrating the mortality model with a jump model that incorporates COVID-19 deaths we constructed a temporary mortality jump model. As a result, the temporary mortality jump model reflects the effects of the pandemic more realistically. We observe that even in this case mortality has a minor impact, whereas interest rates significantly still affect the financial position and performance of insurance companies.

During the late eighteenth and early nineteenth centuries, mutual associations predominated in insuring the large fleet of ships that carried coal from Britain's northeast to London and other ports. The number of associations grew rapidly from the late 1770s, initially on the Tyne, then spreading to other ports on the east coast. They largely saw off the challenge from joint-stock companies created after the liberalisation of the marine insurance market in 1824. Low administrative and legal costs and the ability to mobilise local knowledge to minimise risks allowed the associations to offset the disadvantage of insuring vessels in the same trade facing similar adversities. This article discusses how mutual associations were organised and operated, traces their development on the Tyne and the competition they encountered there from Lloyd's of London and joint-stock insurance companies, and examines the incidence of mutual associations elsewhere in Britain.

We use Benford's law to examine the non-random elements of health care costs. We find that as health care expenditures increase, the conformity to the expected distribution of naturally occurring numbers worsens, indicating a tendency towards inefficient treatment. Government insurers follow Benford's law better than private insurers indicating more efficient treatment. Surprisingly, self-insured patients suffer the most from non-clinical cost factors. We suggest that cost saving efforts to reduce non-clinical expenses should be focused on more severe, costly encounters. Doing so focuses cost reduction efforts on less than 10% of encounters that constitute over 70% of dollars spent on health care treatment.

Reinsurers may default when they have to pay large claims to insurers but are unable to fulfill their obligations due to various reasons such as catastrophic events, underwriting losses, inadequate capitalization, or financial mismanagement. This paper studies the problem of optimal reinsurance design from the perspectives of both the insurer and reinsurer when the insurer faces the potential default risk of the reinsurer. If the insurer aims to minimize the convex distortion risk measure of his retained loss, we prove the optimality of a stop-loss treaty when the promised ceded loss function is charged by the expected value premium principle and the reinsurer offers partial recovery in the event of default. For any fixed premium loading set by the reinsurer, we then derive the explicit expressions of optimal deductible levels for three special distortion functions, including the TVaR, Gini, and PH transform distortion functions. Under these three explicit distortion risk measures adopted by the insurer, we seek the optimal safety loading for the reinsurer by maximizing her net profit where the reserve capital is determined by the TVaR measure and the cost is governed by the expectation. This procedure ultimately leads to the Bowley solution between the insurer and the reinsurer. We provide several numerical examples to illustrate the theoretical findings. Sensitivity analyses demonstrate how different settings of default probability, recovery rate, and safety loading affect the optimal deductible values. Simulation studies are also implemented to analyze the effects induced by the default probability and recovery rate on the Bowley solution.