Form Of Reinsurance Research Articles

Multiperiod peer‐to‐peer risk sharing

AbstractRisk sharing has been practiced in various forms in the financial industry. This paper is the first to study both dynamic and static risk‐sharing mechanisms for a group of participants over multiple periods. The design of risk‐sharing strategies is based on the Pareto optimization of quadratic utilities of participants' reserves. Such a framework builds a connection between portfolio optimization in the finance literature and that for risk sharing in the insurance literature. Building on the most common form of reinsurance—pro rata treaties, we propose a peer‐to‐peer (P2P) network for risk sharing. Assuming independent multivariate losses over time, we find that the optimal risk‐sharing allocation exhibits a three‐component structure with the long‐term limit and two correction terms. This allows us to show convergence of the risk‐sharing solution and the ratios of long‐term reserves. Furthermore, we study the impact of actuarial fairness on various risk‐sharing strategies and their long‐term limits.

Применение финансовых инноваций в системе перестраховочной защиты: опыт развитых стран и перспективы для России

The article examines the prospects for the application of financial innovations in the reinsurance protection system in Russia, taking into account global experience. The growing need to modernize the Russian reinsurance market in the context of financial globalization and increased external constraints is noted. The characteristics of the current state of the national reinsurance system are analyzed, key problems and imbalances are identified. It is shown that traditional forms of reinsurance do not reduce systemic risks in the industry, and dependence on foreign capacity is vulnerable to sanctions pressure. The successful experience of developed countries in using innovative reinsurance tools is considered. A set of measures is proposed for the introduction of financial innovations in Russia through the infrastructural reform of the reinsurance system and the establishment of international cooperation. It is concluded that financial innovations have high potential for increasing the sustainability and competitiveness of the Russian insurance sector.

Catastrophe (CAT) bonds:

Catastrophe bonds, a relatively new entry into the bond market, are a form of reinsurance in which insurance firms are able to offset the financial risks from both natural and man-made catastrophes. Although the primary offset is within the reinsurance market, starting in the 1990s insurance firms started using the financial markets to offset catastrophe risks. Anecdotal evidence shows that the entry of CAT bonds made the reinsurance market more efficient and allowed investors an opportunity to participate in what has been a very profitable investment opportunity. Our analysis shows that on average, CAT bonds have generated high returns but with the advantage of diversification when compared with similarly rated corporate debt. Thus, CAT bonds are a viable investment option withina diversified portfolio.

The Optimal Reinsurance Strategy under Conditional Tail Expectation (CTE) and Wang’s Premium Principle

In this study, we take the conditional tail expectation (CTE) as the constraint condition and consider the optimal reinsurance issues under Wang’s premium principle in general insurance contracts. With the confidence level and the distortion function in Wang’s premium principle given by the insurer in advance, a threshold can be obtained. When the insurer’s risk tolerance level is greater than this value, the optimal reinsurance is a proportional reinsurance in which the deductible equals to this value, else the optimal form of reinsurance is a stop-loss reinsurance. Corresponding numerical examples and economic explanations are also given.

El reaseguro en el riesgo de mortalidad en Solvencia II

The aim of this paper is to analyze the mitigating effect that, for an insurance company, the solvency capital requirement for the mortality risk of the life underwriting risk module has. In our model, the solvency capital required to the insurance company is computed through an internal model based in the Monte Carlo’s simulation method. That capital is obtained as the value in risk at 99,5% of the difference between the present value of assets minus the present value of liabilities corresponding to two consecutive years, where the reinsurance company policy is taken into account for its calculation. The forms of reinsurance considered in the analysis are the quota share, the surplus and the stop-loss. Finally, and for the case of the quota share, a sensitivity analysis of the required solvency capital of the company with respect to the ratio retention is carried out. Furthermore, and for the case of the surplus and stop-loss, a sensitivity analysis with respect to the priority is also made.

Optimality of Reinsurance Treaties under a Mean - Ruin Probability Criterion

The minimization of the probability of ruin is a crucial criterion for determining the effect of the form of reinsurance on the wealth of the cedant and is a very important factor in choosing optimal reinsurance. However, this optimization criterion alone does not generally lead to a rational decision to choose an optimal reinsurance plan. This criterion acts only on the risk (minimizing it via the probability of ruin), but does not affect the technical benefit, that is to say, the insurer should not choose the optimal reinsurance treaty, it is not beneficial.We propose a new reinsurance optimization strategy that maximizes the technical benefit of an insurance company while maintaining a minimal level for the probability of ruin. The objective is to optimize with precision and ease of computation using Genetic algorithms.

Minimizing the probability of ruin: Optimal per-loss reinsurance

We compute the optimal investment and reinsurance strategy for an insurance company that wishes to minimize its probability of ruin, when the risk process follows a compound Poisson process (CPP) and reinsurance is priced via the expected-value premium principle. We consider per-loss optimal reinsurance for the CPP after first determining optimal reinsurance for the diffusion that approximates this CPP. For both the CPP claim process and its diffusion approximation, the financial market in which the insurer invests follows the Black–Scholes model, namely, a single riskless asset that earns interest at a constant rate and a single risky asset whose price process follows a geometric Brownian motion. Under minimal assumptions about admissible forms of reinsurance, we show that optimal per-loss reinsurance is excess-of-loss. Therefore, our result extends the work of the optimality of excess-of-loss reinsurance to the problem of minimizing the probability of ruin.

Optimal Reinsurance through Minimizing New Risk Measures under Technical Benefit Constraints

In this paper we present an approach to minimize the actuarial risk for the optimal choice of a form of reinsurance, and this is intended to be through a choice of treated parameters that minimize the risk using the Conditional Tail Expectation and the Conditional Tail Variance risk measures. The minimization procedure is based on the Augmented Lagrangian and a genetic algorithm with technical benefit as a constraint. This approach can be seen as a decision support tool that can be used by managers to minimize the actuarial risk in the insurance company.

The Optimization of Reinsurance by the Maximization of Technical Benefits and Minimization of Probability of Ruin Using Genetic Algorithms

The ruin theory is a crucial tool for the insurance company and it is a very important factor in choosing an optimal reinsurance. However this single optimization criterion does not usually lead to a rational decision to choose an optimal reinsurance plan. In this paper, we propose an approach for optimizing a reinsurance strategy which is based on maximizing technical benefit of the insurer and the minimization of the probability of ruin simultaneously and dynamically using genetic algorithms. This approach uses a database that contains the forms of reinsurance and pricing methods. This work is a decision support tool for insurance companies.

Reinsurance by short-term reinsurers in South Africa

The short-term reinsurance process usually involves three parties, namely the insurer, the reinsurer and the original policyholder, as the insurer cedes a part of the covered risk of the policyholder to the reinsurer. This research however addresses the perceptions of reinsurers regarding their reinsurance activities, where the reinsurer sells reinsurance to other insurance entities (viz. insurers and reinsurers), as well as buys reinsurance from other insurance entities. The crux of short-term reinsurance is therefore mutually loss sharing between the various insurance entities. The objective of this research focuses on the improvement of financial decision-making regarding the reinsurance operations of the reinsurers. To achieve this objective a literature study was undertaken to provide adequate background to compile a questionnaire for the empirical survey. The primary study embodies the perceptions of the South African short-term reinsurers regarding the following aspects: the various reasons why reinsurance occurs; the contracts / methods of reinsurance; the bases / forms of reinsurance; and the factors which determine the retention levels of a reinsurer. South Africa is classified as a developing economy, is a member of the BRICS countries and has an emerging market economy. The empirical results should therefore also be valuable to other countries which are classified similarly.

OPTIMAL REINSURANCE FROM THE PERSPECTIVES OF BOTH AN INSURER AND A REINSURER

AbstractOptimal reinsurance from an insurer's point of view or from a reinsurer's point of view has been studied extensively in the literature. However, as two parties of a reinsurance contract, an insurer and a reinsurer have conflicting interests. An optimal form of reinsurance from one party's point of view may be not acceptable to the other party. In this paper, we study optimal reinsurance designs from the perspectives of both an insurer and a reinsurer and take into account both an insurer's aims and a reinsurer's goals in reinsurance contract designs. We develop optimal reinsurance contracts that minimize the convex combination of the Value-at-Risk (VaR) risk measures of the insurer's loss and the reinsurer's loss under two types of constraints, respectively. The constraints describe the interests of both the insurer and the reinsurer. With the first type of constraints, the insurer and the reinsurer each have their limit on the VaR of their own loss. With the second type of constraints, the insurer has a limit on the VaR of his loss while the reinsurer has a target on his profit from selling a reinsurance contract. For both types of constraints, we derive the optimal reinsurance forms in a wide class of reinsurance policies and under the expected value reinsurance premium principle. These optimal reinsurance forms are more complicated than the optimal reinsurance contracts from the perspective of one party only. The proposed models can also be reduced to the problems of minimizing the VaR of one party's loss under the constraints on the interests of both the insurer and the reinsurer.

Optimizing the technical benefits of the insurance company using genetic algorithms

In this paper, we present a new method for dynamic optimization to achieve maximum technical benefit to the insurer using genetic algorithms. The objective of this work is to select, from a database containing forms of reinsurance, pricing models and credit ratings parameters (risk measurement methods, such as Value at Risk (VaR), Conditional Value at Risk (CVaR) or ruin probability) a form of reinsurance, a way of pricing and a solvency parameter to maximize technical benefits of the insurance company.

OPTIMIZATION OF SOME REINSURANCE STRATEGIES

The basic purpose of the work is a study of existing approaches to reinsurance directed towards modeling of distribution and minimization of risk for an insurance portfolio, and forming a strategy for its optimal reinsurance using developed decision support system. A method for a search of optimal reinsurance strategy is proposed. For this purpose statistical models were selected that correspond to the structure and volume of portfolio losses as well as the number of these losses. The simulation model for the total insurance losses is developed. While finding an optimal reinsurance strategy it was taken into consideration the dependence of the load coefficient on a specific form of reinsurance. A numerical study of the dependence between optimal reinsurance strategy and the varying load coefficient has been performed. It was established that taking into consideration of the variable load coefficient for specific risk capital values for an insurance company the stop-loss strategy provides worse results than other forms considered. An architecture and the functional layout for decision support system are proposed, and appropriate software was developed in C#. The decision support system functioning has been illustrated on simulated example. The system will provide a useful instrument for a business analytic to support decision making while selecting a strategy for insurance portfolio in specific conditions.

Optimal Dynamic Risk Control for Insurers with State-Dependent Income

In this paper we investigate optimal forms of dynamic reinsurance polices among a class of general reinsurance strategies. The original surplus process of an insurance portfolio is assumed to follow a Markov jump process with state-dependent income. We assume that the insurer uses a dynamic reinsurance policy to minimize the probability of absolute ruin, where the traditional ruin can be viewed as a special case of absolute ruin. In terms of approximation theory of stochastic process, the controlled diffusion model with a general reinsurance policy is established strictly. In such a risk model, absolute ruin is said to occur when the drift coefficient of the surplus process turns negative, when the insurer has no profitability any more. Under the expected value premium principle, we rigorously prove that a dynamic excess-of-loss reinsurance is the optimal form of reinsurance among a class of general reinsurance strategies in a dynamic control framework. Moreover, by solving the Hamilton-Jacobi-Bellman equation, we derive both the explicit expression of the optimal dynamic excess-of-loss reinsurance strategy and the closed-form solution to the absolute ruin probability under the optimal reinsurance strategy. We also illustrate these explicit solutions using numerical examples.

Optimal Dynamic Risk Control for Insurers with State-Dependent Income

In this paper we investigate optimal forms of dynamic reinsurance polices among a class of general reinsurance strategies. The original surplus process of an insurance portfolio is assumed to follow a Markov jump process with state-dependent income. We assume that the insurer uses a dynamic reinsurance policy to minimize the probability of absolute ruin, where the traditional ruin can be viewed as a special case of absolute ruin. In terms of approximation theory of stochastic process, the controlled diffusion model with a general reinsurance policy is established strictly. In such a risk model, absolute ruin is said to occur when the drift coefficient of the surplus process turns negative, when the insurer has no profitability any more. Under the expected value premium principle, we rigorously prove that a dynamic excess-of-loss reinsurance is the optimal form of reinsurance among a class of general reinsurance strategies in a dynamic control framework. Moreover, by solving the Hamilton-Jacobi-Bellman equation, we derive both the explicit expression of the optimal dynamic excess-of-loss reinsurance strategy and the closed-form solution to the absolute ruin probability under the optimal reinsurance strategy. We also illustrate these explicit solutions using numerical examples.

Optimal Dynamic Risk Control for Insurers with State-Dependent Income

In this paper we investigate optimal forms of dynamic reinsurance polices among a class of general reinsurance strategies. The original surplus process of an insurance portfolio is assumed to follow a Markov jump process with state-dependent income. We assume that the insurer uses a dynamic reinsurance policy to minimize the probability of absolute ruin, where the traditional ruin can be viewed as a special case of absolute ruin. In terms of approximation theory of stochastic process, the controlled diffusion model with a general reinsurance policy is established strictly. In such a risk model, absolute ruin is said to occur when the drift coefficient of the surplus process turns negative, when the insurer has no profitability any more. Under the expected value premium principle, we rigorously prove that a dynamic excess-of-loss reinsurance is the optimal form of reinsurance among a class of general reinsurance strategies in a dynamic control framework. Moreover, by solving the Hamilton-Jacobi-Bellman equation, we derive both the explicit expression of the optimal dynamic excess-of-loss reinsurance strategy and the closed-form solution to the absolute ruin probability under the optimal reinsurance strategy. We also illustrate these explicit solutions using numerical examples.

Longevity risk, cost of capital and hedging for life insurers under Solvency II

The cost of capital is an important factor determining the premiums charged by life insurers issuing life annuities. This capital cost can be reduced by hedging longevity risk with longevity swaps, a form of reinsurance. We assess the costs of longevity risk management using indemnity based longevity swaps compared to costs of holding capital under Solvency II. We show that, using a reasonable market price of longevity risk, the market cost of hedging longevity risk for earlier ages is lower than the cost of capital required under Solvency II. Longevity swaps covering higher ages, around 90 and above, have higher market hedging costs than the saving in the cost of regulatory capital. The Solvency II capital regulations for longevity risk generates an incentive for life insurers to hold longevity tail risk on their own balance sheets, rather than transferring this to the reinsurance or the capital markets. This aspect of the Solvency II capital requirements is not well understood and raises important policy issues for the management of longevity risk.

Longevity Risk, Cost of Capital and Hedging for Life Insurers Under Solvency II

The cost of capital is an important factor determining the premiums charged by life insurers issuing life annuities. Insurers will be able to offer more finely priced annuities if they can reduce this cost whilst maintaining solvency. This capital cost can be reduced by hedging longevity risk with longevity swaps, a form of reinsurance. We assess the costs of longevity risk management using longevity swaps compared to costs of holding capital under Sovency II. We show that, using a reasonable market price of longevity risk, the market cost of hedging longevity risk for earlier ages is lower than the cost of capital required under Solvency II. Longevity swaps covering higher ages, around 90 and above, have higher market hedging costs than the saving in the cost of regulatory capital. The Solvency II capital regulations for longevity risk generates an incentive for life insurers to hold longevity tail risk on their own balance sheets rather than transfer this to the reinsurance or the capital markets. This aspect of Solvency II capital requirements is not well understood and raises important policy issues for the management of longevity risk.

Optimal reinsurance arrangements in the presence of two reinsurers

In this paper, we investigate the optimal form of reinsurance from the perspective of an insurer when he decides to cede part of the loss to two reinsurers, where the first reinsurer calculates the premium by expected value principle while the premium principle adopted by the second reinsurer satisfies three axioms: distribution invariance, risk loading, and preserving stop-loss order. In order to exclude the moral hazard, a typical reinsurance treaty assumes that both the insurer and reinsurers are obligated to pay more for the larger loss. Under the criterion of minimizing value at risk (VaR) or conditional value at risk (CVaR) of the insurer's total risk exposure, we show that an optimal reinsurance policy is to cede two adjacent layers, where the upper layer is distributed to the first reinsurer. To further illustrate the applicability of our results, we derive explicitly the optimal layer reinsurance by assuming a generalized Wang's premium principle to the second reinsurer.

Self Insurance for Small Employers Under the Affordable Care Act: Federal and State Regulatory Options

As implementation of the Affordable Care Act reshapes the US health insurance market, state and federal policy makers should be prepared to revisit regulation of stop-loss coverage — a form of reinsurance — for small businesses. Aspects of the reform law could motivate small businesses to self-insure, rather than participate in state-regulated markets either inside or outside the new health insurance exchanges. If younger or healthier groups self-insure, premiums for insured plans will rise, perhaps to an extent that could seriously impair the regulated market. State or federal lawmakers can influence small businesses to participate in the regulated market by making it more difficult or costly to obtain stop-loss coverage, which self-funded employers rely on to protect their businesses from catastrophic medical costs incurred by one or more insured workers. Regulators can limit the comprehensiveness of stop-loss coverage, ban stop-loss coverage outright, or regulate it as they do primary coverage. Because the issues are national in scope, and because uncertainty over ERISA preemption complicates state initiative, the federal government should take the lead in determining the proper confines of self-funding in the small-group employer market.