Reinsurance Arrangements Research Articles

Optimal Reinsurance Arrangement Under Heterogeneous Beliefs: A Unified Method with Piecewise Modification

Optimal Reinsurance Arrangement Under Heterogeneous Beliefs: A Unified Method with Piecewise Modification

Regulatory capital and asset risk transfer

AbstractWe explore whether life insurers use a unique reinsurance arrangement to manage assets tied to their regulatory capital. Typical reinsurance allows insurers to reduce their regulatory capital by transferring liabilities (reserves), and the associated assets, to reinsurers. With modified coinsurance (ModCo), insurers maintain control of their liabilities and assets while transferring regulatory capital requirements to the reinsurer. Holding fixed an insurer's reported capital, we find that ModCo allows insurers to report higher risk‐based capital ratios. Insurers with ModCo are less likely to fire sale downgraded bonds. We also find suggestive evidence of regulatory arbitrage, as most ModCo is purchased from reinsurers in countries with low capital requirements or within the same insurance group.

Multiple per-claim reinsurance based on maximizing the Lundberg exponent

In this paper, we consider the optimal per-claim reinsurance problem for an insurer who designs a reinsurance contract with multiple reinsurance participants. In contrast to using the value-at-risk as a short-term risk measure, we take the Lundberg exponent in risk theory as a risk measure for the insurer over a long-term horizon because the Lundberg upper bound performs better in measuring the infinite-time ruin probability. To reflect various risk preferences of the reinsurance participants, we adopt a type of combined premium principle in which the expected premium principle, variance premium principle, and exponential premium principle are all special cases. Based on maximization of the insurer's Lundberg exponent, the optimal reinsurance is formulated within a static setting, and we derive optimal multiple reinsurance strategies within a general admissible policies set. In general, these optimal strategies are shown to have non-piecewise linear structures, differing from conventional reinsurance strategies such as quota-share, excess-of-loss, or linear layer reinsurance arrangements. In some special cases, the optimal reinsurance strategies reduce to classical results.

REINSURANCE ARRANGEMENTS ASSOCIATED WITH GUARANTEE LEGAL RESPONSIBILITIES

The use of diversion responsibility or reinsurance arrangements as a way for insurance companies to protect themselves from losses by cooperating with a reinsurance company. One reason for utilizing reinsurance is to distribute risk. Reinsurance becomes more understandable when insurance claims occur, and it is not possible to have reinsurance without having insurance first. The legal framework for insurance and reinsurance is explained in the Criminal Code or Law Number 40 of 2014 concerning business insurance. However, there is no provision that clearly defines what is meant by reinsurance, which can cause problems if there are insufficient answers regarding the company's reinsurance payment for losses. Therefore, legal certainty is necessary. The research objective is to determine the form of responsibility of the guarantor in reinsurance, and the normative law method is used. The Ex-Gratia Payment clause outlines the responsibility of the reinsurance company to the insured, allowing the insured to claim compensation from the insurer for reinsurance claims.

Risk Management at a Time of Systemic Uncertainty: Transfer Pricing Implications of Intra-Group Reinsurance Quota Share Arrangements

This study addresses an underexplored and highly topical area regarding the international tax implications of risk management, examining some core methodological questions surrounding the transfer pricing aspects of intra-group reinsurance in depth. The study first provides an overview of traditional property and casualty reinsurance risk transfer structures. It then focuses, in particular, on proportional quota share reinsurance arrangements in both external and intra-group settings. Additionally, it highlights the key entrepreneurial risk-taking functions in the insurance sector and examines potential transfer pricing remuneration methods for quota share reinsurance arrangements in intra-group transactions. The latter points are illustrated through case studies.

Knowledge Learning of Insurance Risks Using Dependence Models

Learning the customers’ experience and behavior creates competitive advantages for any company over its rivals. The insurance industry is an essential sector in any developed economy and a better understanding of customers’ risk profile is critical to decision making in all aspects of insurance operations. In this paper, we explore the idea of using copula-based dependence models to learn the hidden risk of policyholders in property insurance. Specifically, we build a novel copula model to accommodate the dependence over time and over space among spatially clustered property risks. To tackle the computational challenge caused by the discreteness feature of large-scale insurance data, we propose an efficient multilevel composite likelihood approach for parameter estimation. Provided that latent risk induces correlation, the proposed customer learning method offers improved predictive analytics by allowing insurers to borrow strength from related risks in predicting new risks and also helps reveal the relative importance of the multiple sources of unobserved heterogeneity in updating policyholders’ risk profile. In the empirical study, we examine the loss cost of a portfolio of entities insured by a government property insurance program in Wisconsin. We find both significant temporal and spatial association among property risks. However, their effects on the predictive distribution of loss cost are different for the new and renewal policyholders. The two sources of dependence are complements for the former and substitutes for the latter. These findings are shown to have substantial managerial implications in key insurance operations such as experience rating, capital allocation, and reinsurance arrangement.

Optimal Reinsurance Minimizing the Absolute Value of the Difference between the Profits of the Insurer and the Reinsurer

Many optimal reinsurance studies in the literature only take into consideration the insurer. However, there are two parties in reinsurance contracts. The aim of the study is to contribute to the optimal reinsurance literature by considering the interests of both the insurer and the reinsurer. A reasonable compromise between their interests is desired. Then, we examine the optimal retention problem that minimizes the absolute value of the difference between the insurer’s and the reinsurer’s profits under stop-loss and excess-of-loss reinsurance arrangements. With a non-negative random variable, we incorporate the stochastic essence of the aggregate loss for the reinsurer’s and insurer’s profits into the model. For reinsurance premium calculation we use two different premium principles and for aggregate loss we use exponential, Pareto and lognormal distributions. The results of the studies only deal with the benefits of the insurer and the studies consider both the benefits of the insurer and reinsurer are compared. Our findings can be helpful for insurance companies and reinsurer companies in their decision making task. For simulation studies in the model MATLAB programming language is used.

Impact of Reinsurance on Performance of Nepalese Insurance Companies

Reinsurance is considered as backbone of the insurance industry in developed and developing countries as it indirectly injects capital and Nepalese insurance companies are no exception. Thus, this study is aims to find out whether the use of reinsurance arrangement lead to positive effect or not? Three portfolios have been formed life, nonlife and industry. The study used 11 years unbalanced cross sectional secondary data from 2007/08 to 2017/18. The sample of the study consists of seven from life and nine from nonlife with 138 firm years’ observations. The dependent variable performance is measured by profitability (ROA and ROE) and solvency while reinsurance ceded as explanatory variable. Capital employed and size of the firm are considered as control variables. The study employed descriptive cum causal comparative research design. Regression analysis has been performed to see the effect of reinsurance on firm performance. The result depicts that reinsurance has a positive and significant impact on performance of insurance companies. This finding indicates that reinsurance improves the cost efficiency of primary insurers. Further, reinsurance is a complement for capital in order to enhance solvency while negative relation indicating solvency of the insurers increases with the level of used reinsurance, to the extent that reinsurance and capital can be substitutes of each other. Thus, this study concludes that primary insurers can benefit from reinsurance as its relief on capital, diversify risk and in turn helps to earn profitability by sharing the risk with reinsurers. Key words: Reinsurance, Profitability, Solvency, Capital, Premium

Premium Risk Net of Reinsurance: From Short-Term to Medium-Term Assessment

Solvency II requirements introduced new issues for actuarial risk management in non-life insurance, challenging the market to have a consciousness of its own risk profile, and also investigating the sensitivity of the solvency ratio depending on the insurance risks and technical results on either a short-term and medium-term perspective. For this aim, in the present paper, a partial internal model for premium risk is developed for three multi-line non-life insurers, and the impact of some different business mixes is analyzed. Furthermore, the risk-mitigation and profitability impact of reinsurance in the premium risk model are introduced, and a global framework for a feasible application of this model consistent with a medium-term analysis is provided. Numerical results are also figured out with evidence of various effects for several portfolios and reinsurance arrangements, pointing out the main reasons for these differences.

An Iterated Bornhuetter-Ferguson Model

The iterated Bornhuetter-Ferguson loss reserving method generates an infinite sequence of reserve formulas, with the chain ladder and Bornhuetter-Ferguson formulas at opposite extremes. The sequence also contains the Benktander-Hovinen formula. Although the literature contains parametric stochastic models for the first two of these three, it does not contain models for the remainder of the sequence. The present paper fills this gap with a sequence of Bayesian chain ladder models, one for each iterate. Each is an ODP chain ladder model, with each row parameter drawn from a gamma prior. The parameters vary from iterate to iterate. Equality between each Bayesian chain ladder model and its corresponding iterate is achieved by suitable choice of the coefficients of variation of the row parameters. Thus, each iterate is a special case of the general Gamma-ODP model. Applications of this sequence of models are illustrated, first the application of the sequence of Bayesian chain ladder models directly to loss reserving, and second to a hierarchy of proportional reinsurance arrangements. In the first of these applications, the parameter selection for the Gamma-ODP special cases will not always be natural or intuitive. The use of the general Gamma-ODP model with more natural parameter values may be preferable.

ON A NEW PARADIGM OF OPTIMAL REINSURANCE: A STOCHASTIC STACKELBERG DIFFERENTIAL GAME BETWEEN AN INSURER AND A REINSURER

AbstractThis paper proposes a new continuous-time framework to analyze optimal reinsurance, in which an insurer and a reinsurer are two players of a stochastic Stackelberg differential game, i.e., a stochastic leader-follower differential game. This allows us to determine optimal reinsurance from joint interests of the insurer and the reinsurer, which is rarely considered in the continuous-time setting. In the Stackelberg game, the reinsurer moves first and the insurer does subsequently to achieve a Stackelberg equilibrium toward optimal reinsurance arrangement. Speaking more precisely, the reinsurer is the leader of the game and decides on an optimal reinsurance premium to charge, while the insurer is the follower of the game and chooses an optimal proportional reinsurance to purchase. Under utility maximization criteria, we study the game problem starting from the general setting with generic utilities and random coefficients to the special case with exponential utilities and constant coefficients. In the special case, we find that the reinsurer applies the variance premium principle to calculate the optimal reinsurance premium and the insurer's optimal ceding/retained proportion of insurance risk depends not only on the risk aversion of itself but also on that of the reinsurer.

Fit for Purpose and Fit for the Future? An Evaluation of the UK's New Flood Reinsurance Pool

AbstractFlood Re is widely hailed as an innovative approach to disaster risk insurance. This article offers a mixed‐methods evaluation of the new pool, asking whether it is “fit for purpose” and “fit for the future.” The investigation considers the roles of the public and private sectors, risk modeling and risk communication, technical underwriting, distributional aspects, and the behavioral implications of Flood Re, particularly with regards to risk reduction and prevention. The article concludes that the new pool is a transitional reinsurance arrangement that supports the private insurance market and secures affordability of flood insurance in the United Kingdom through premium subsidies. However, this approach is likely to come under pressure in the face of rising flood risk as it fails to incentivize flood risk management and risk reduction efforts.

Pareto-optimal reinsurance arrangements under general model settings

In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. For the purpose of practice, we use numerical examples to show how to determine the mutually acceptable Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer’s aim and the reinsurer’s goal can be met under the mutually acceptable Pareto-optimal reinsurance contracts.

De Vylder approximation to the optimal retention for a combination of quota-share and excess of loss reinsurance with partial information

This paper considers the optimal retention in a combination of quota-share and excess of loss reinsurance. Assuming that the insurer only has partial information of the individual claim size, we develop the De Vylder approximation for the insurer’s ultimate ruin probability. To fulfill the requirement of De Vylder approximation, the translated gamma approximation is adopted for approximating the received premium and the first three moments of the claim size (after reinsurance) for the insurer. We then derive the optimal retention for the reinsurance arrangement by minimizing the approximated ruin probability. For illustration purpose, some numerical examples are included to show the impact of partial information on the approximated ruin probability as well as the optimal retention.

Optimal Reinsurance Under the Risk-Adjusted Value of an Insurer’s Liability and an Economic Reinsurance Premium Principle

In this article, an optimal reinsurance problem is formulated from the perspective of an insurer, with the objective of minimizing the risk-adjusted value of its liability where the valuation is carried out by a cost-of-capital approach and the capital at risk is calculated by either the value-at-risk (VaR) or conditional value-at-risk (CVaR). In our reinsurance arrangement, we also assume that both insurer and reinsurer are obligated to pay more for a larger realization of loss as a way of reducing ex post moral hazard. A key contribution of this article is to expand the research on optimal reinsurance by deriving explicit optimal reinsurance solutions under an economic premium principle. It is a rather general class of premium principles that includes many weighted premium principles as special cases. The advantage of adopting such a premium principle is that the resulting reinsurance premium depends not only on the risk ceded but also on a market economic factor that reflects the market environment or the risk the reinsurer is facing. This feature appears to be more consistent with the reinsurance market. We show that the optimal reinsurance policies are piecewise linear under both VaR and CVaR risk measures. While the structures of optimal reinsurance solutions are the same for both risk measures, we also formally show that there are some significant differences, particularly on the managing tail risk. Because of the integration of the market factor (via the reinsurance pricing) into the optimal reinsurance model, some new insights on the optimal reinsurance design could be gleaned, which would otherwise be impossible for many of the existing models. For example, the market factor has a nontrivial effect on the optimal reinsurance, which is greatly influenced by the changes of the joint distribution of the market factor and the loss. Finally, under an additional assumption that the market factor and the loss have a copula with quadratic sections, we demonstrate that the optimal reinsurance policies admit relatively simple forms to foster the applicability of our theoretical results, and a numerical example is presented to further highlight our results.

Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account

Optimal forms of reinsurance policies have been studied for a long time in the actuarial literature. Most existing results are from the insurer’s point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement that might be very attractive to one party (e.g., the insurer) can be quite unacceptable to the other party (e.g., the reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party’s risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaR s of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values.

Pareto-Optimal Reinsurance Arrangements Under General Model Settings

In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. From the purpose of practice, we use numerical examples to show how to determine the best Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer's aim and the reinsurer's goal can be met under the best Pareto-optimal reinsurance contracts.

A comparison of risk transfer strategies for a portfolio of life annuities based on RORAC

ABSTRACTThis paper aims to compare different reinsurance arrangements in order to reduce the longevity and financial risk originated by a life insurer while managing a portfolio of annuities policies. Linear and nonlinear reinsurance strategies as well as swap like agreements are evaluated via a discrete-time actuarial risk model. Specifically, longevity dynamics are represented by Lee–Carter type models, while interest rate is modeled by Cox–Ingersoll–Ross model. The reinsurance strategies effectiveness is evaluated according to the Return on Risk Adjusted Capital under a ruin probability constrain.

Optimal Reinsurance Policies When the Interests of Both the Cedent and the Reinsurer are Taken into Account

Optimal forms of reinsurance policies have been studied for a long time in actuarial literature. Most existing results are from the insurer's point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement which might be very attractive to one party (e.g., insurer) can be quite unacceptable to the other party (e.g., reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party's risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaRs of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values.

Optimal reinsurance policies with two reinsurers in continuous time

An optimal reinsurance problem of an insurer is studied in a continuous-time model, where insurance risk is partly transferred to two reinsurers, one adopting the expected-value premium principle and another one using the variance premium principle. The insurer aims to select an optimal reinsurance arrangement to minimize the probability of ruin. To provide an easy-to-implement solution to the problem, (semi)-explicit expressions for the optimal reinsurance strategies as well as the minimal ruin probabilities are derived for several claims distributions. Numerical studies including a real-data example based on the Danish fire insurance losses are provided to illustrate the solution of the problem. Our empirical results based on the Danish data reveal that the heavy-right-tailedness of claims distributions has a significant impact on the optimal reinsurance strategies and has a quite pronounced impact on the residual risk described by the minimal ruin probability.