Excess of loss reinsurance under joint survival optimality

Explicit expressions for the probability of joint survival up to time x of the cedent and the reinsurer, under an excess of loss reinsurance contract with a limiting and a retention level are obtained, under the reasonably general assumptions of any non-decreasing premium income function, Poisson claim arrivals and continuous claim amounts, modelled by any joint distribution. By stating appropriate optimality problems, we show that these results can be used to set the limiting and the retention levels in an optimal way with respect to the probability of joint survival. Alternatively, for fixed retention and limiting levels, the results yield an optimal split of the total premium income between the two parties in the excess of loss contract. This methodology is illustrated numerically on several examples of independent and dependent claim severities. The latter are modelled by a copula function. The effect of varying its dependence parameter and the marginals, on the solutions of the optimality problems and the joint survival probability, has also been explored

Moral Hazard in Reinsurance Markets

This paper attempts to identify moral hazard in the traditional reinsurance market. We build a multi-period principle agent model of the reinsurance transaction from which we derive predictions on premium design, monitoring, loss control and insurer risk retention. We then use panel data on U.S. property liability reinsurance to test the model. The empirical results are consistent with the model's predictions. In particular, we find evidence for the use of loss sensitive premiums when the insurer and reinsurer are not affiliates (i.e., not part of the same financial group), but little or no use of monitoring. In contrast, we find evidence for the use of monitoring when the insurer and reinsurer are affiliates, where monitoring costs are lower, but little use of price controls.

Financial Innovation in the Management of Catastrophe Risk

Catastrophic events such as hurricane and earthquakes are the dominant source of risk for many property casualty insurers. Primary insurers usually limit the scale and geographic scope of their operations in order to focus on core competencies such as marketing, underwriting and loss control. But his often leaves them without sufficient geographic spread to diversify catastrophe risk. The traditional hedge for the primary insurer is reinsurance. Specialist reinsurers achieve a spacial spread of risk and can therefore bear catastrophe risk that is undiversifiable to the primary. But the transaction costs associated with reinsurance, and therefore premiums, are high. High premiums, coupled with the fact that catastrophe losses exhibit little correlation with capital market indices, has attracted considerable activity in Wall Street in searching for new instruments that securitize catastrophe risk. Indeed many players are now talking of catastrophe risk being a new “asset class” and new instruments such as catastrophe options and catastrophe bonds are starting to appear. The rationale for these new instruments is usually developed as follows. Recent catastrophe events such as Hurricane Andrew and the Northridge earthquake have imposed costs on the insurance industry of an order of magnitude not thought possible only a decade ago. More sophisticated modeling now presents potential losses to the industry of $50 billion or more. Examples would be Andrew hitting Miami, a major quake on the New Madrid Fault and a repeat of the 1906 San Francisco earthquake. These events could wipe out 25$200 billion. Two such events, or one such event combined with continued mass tort claims (e.g. successful plaintiff claims in tobacco litigation) could cripple the whole industry. However, losses of this size would hardly cause a ripple in capital markets. The U.S. capital market currently currently consists of securities representing some $13 trillion of investor wealth and the loss scenarios cited above amount to less than one standard deviation of daily trading volume. Presentations by merchant bankers, reinsurance brokers and others have echoed this potential for diversifying catastrophe risk within the capital market. The high transactions costs of reinsurance offers potential for hedging instruments to be offered to primary insurers that are both competitive with current reinsurance and which offer investors high rates of return. Moreover, since catastrophe risk is uncorrelated with market indices, the benchmark for such investments is just the risk free rate. Pricing new instruments requires that the expected loss be estimated with some. Until recently, insurers and reinsurers had a comparative advantage in information on catastrophic events. But in the past decade a number of modeling firms have developed models that combine seismic and meteorological information with data on the construction, siting, and value of individual buildings. These models can be used to simulate the economic effects of many thousands of storms and earthquakes. Although such models are used by the insurance firms and reinsurers, mainly for loss estimation and re-balancing their exposure, the same models are now available to other companies and investors. The arrival of the modelers and their models is eroding the comparative information advantage of insurers and reinsurers and opening the door to new players. Insurers will retain their comparative advantage over, say, merchant banks in related insurance services such as marketing, underwriting and loss settlement facilities. But the stage has been set for an unbundling of insurance products with insurers retaining marketing underwriting and settlement services and risk bearing by-passing the reinsurance industry and being provided more directly from the capital market. But the combination of high transaction costs for reinsurance and the vast capacity of the capital market for diversification, is not sufficient to ensure the success of these new instruments. The costs associated with reinsurance do not necessarily reflect monopoly rent. Relationships between primary insurers and reinsurers involve moral hazard; the relationship relaxes the incentive for the insurer to underwrite carefully or to settle claims efficiently. Consequently, the reinsurer will monitor the primary. Moreover, long term relationships are often formed to counter such expropriation. The apparently high transaction costs of reinsurance may simply reflect the resolution of moral hazard. If new instruments such as catastrophe options and bonds are to compete successfully with reinsurance, they must be able resolve incentive conflicts between the primary insurer and the ultimate risk bearer. Indeed, if moral hazard is not resolved, using past insurance loss data to estimate the potential returns for purchasers of catastrophe bonds, etc, is spurious. The purpose of this paper is to examine and categorize new catastrophe hedging instruments. These instruments will then be compared with traditional risk management strategies adopted by primary insurers in order to compare their relative efficiency at resolving incentive conflicts. Each instrument offers a different combination of credit risk, basis risk and moral hazard. For example, catastrophe reinsurance is subject to significant credit risk and moral hazard, but does not encounter significant basis risk. I will argue that the differential performance of the traditional and new instruments offers primary insurers with a richer portfolio of risk management strategies, though no strategy is dominant in its performance on all three criteria.

On the Pricing of Intermediated Risks: Theory and Application to Catastrophe Reinsurance

We model the equilibrium price and quantity of risk transfer between firms and financial intermediaries. Value-maximizing firms have downward sloping demands to cede risk, while intermediaries, who assume risk, provide less-than-fully-elastic supply. We show that equilibrium required returns will be "high" in the presence of financing imperfections that make intermediary capital costly. Moreover, financing imperfections can give rise to intermediary market power, so that small changes in financial imperfections can give rise to large changes in price. We develop tests of this alternative against the null that the supply of intermediary capital is perfectly elastic. We take the US catastrophe reinsurance market as an example, using detailed data from Guy Carpenter & Co., covering a large fraction of the catastrophe risks exchanged during 1970-94. Our results suggest that the price of reinsurance generally exceeds "fair" values, particularly in the aftermath of large events, that market power of reinsurers is not a complete explanation for such pricing, and that reinsurers' high costs of capital appear to play an important role.

Integrated asset liability modelling for property casuality insurance : a portfolio theoretical approach

In this paper we have developed a financial model of the non-life insurer to provide assistance for the management of the insurance company in making decisions on product, investment and reinsurance mix. The model is based on portfolio theory and recognizes the stochastic nature of and the interaction between the underwriting and investment income of the insurance business. In the context of an empirical application we illustrate howa portfolio optimisation approach can be used for asset-liability management

Hedging Brevity Risk with Mortality-based Securities

In 2003, Swiss Re introduced a mortality-based security designed to hedge excessive mortality changes for its life book of business. The concern was apparently brevity risk, i.e., the risk of premature death. The brevity risk due to a pandemic is similar to the property risk associated with catastrophic events such as earthquakes and hurricanes and the security used to hedge the risk is similar to a CAT bond. This work looks at the incentives associated with insurance-linked securities. It considers the trade-offs an insurer or reinsurer faces in selecting a hedging strategy. We compare index and indemnity-based hedging as alternative design choices and ask which is capable of creating the greater value for shareholders. Additionally, we model an insurer or reinsurer that is subject to insolvency risk, which creates an incentive problem known as the judgment proof problem. The corporate manager is assumed to act in the interests of shareholders and so the judgment proof problem yields a conflict of interest between shareholders and other stakeholders. Given the fact that hedging may improve the situation, the analysis addresses what type of hedging tool would be best to use. We show that an indemnity-based security tends to worsen the situation, as it introduces an additional incentive problem. Index-based hedging, on the other hand, under certain conditions turns out to be beneficial and therefore clearly dominates indemnity-based strategies. This result is further supported by showing that for the same strike prices the current shareholder value is greater with the index-based security than the indemnity-based security

Surplus sharing with coherent utility functions

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e. the shareholders

Disaster Insurance or a Disastrous Insurance – Natural Disaster Insurance in France

We model natural disaster insurance in France. We explicitly take into account the main institutional features of the system, such as the uniform premium rate in both high and low risk regions and the existence of a state reinsurance company. Our model indicates that the institutional set-up is fundamentally flawed. We find that the market is likely to lead to “specialist” equilibria, where insurers specialize in serving either high or low risk regions. As a result the reinsurance company, which offers cover to all insurers at the same price, is likely to suffer from a portfolio with mainly “bad” risks. We show that increasing the premium rate customers have to pay, a policy undertaken by the French authorities, will not necessarily solve these problems and comes at a high cost to the final consumer (and taxpayer).property insurance, reinsurance, risk selection

ART Versus Reinsurance: The Disciplining Effect of Information Insensitivity

We provide a novel benefit of "Alternative Risk Transfer" (ART) products with parametric or index triggers. When a reinsurer has private information about his client's risk, outside reinsurers will price their reinsurance offer less aggressively. Outsiders are subject to adverse selection as only a high-risk insurer might find it optimal to change reinsurers. This creates a hold-up problem that allows the incumbent to extract an information rent. An information-insensitive ART product with a parametric or index trigger is not subject to adverse selection. It can therefore be used to compete against an informed reinsurer, thereby reducing the premium that a low-risk insurer has to pay for the indemnity contract. However, ART products exhibit an interesting fate in our model as they are useful, but not used in equilibrium because of basis-risk.Cat Bonds, Risk Transfer, Index Trigger, Adverse Selection