The Design of Private Reinsurance Contracts

This article examines the effect of asymmetric information on the trading of underwriting risk between insurers and reinsurers and how it is mitigated in a context of long-term relationships. It begins by explaining how information problems affect the efficiency of the allocation of risk between insurers and reinsurers and how long-term implicit contracts allow the inclusion of new information in the pricing of reinsurance coverage. A key feature of these relationships is the reliance on loss-contingent rebates and commissions in the pricing of reinsurance coverage. We argue that when information is revealed only over time, long-term implicit contracts between insurers and reinsurers allow the inclusion of new information into reinsurance pricing. Because of this feature, the allocation of risk between insurers and reinsurers is more efficient. Specifically, such arrangements lead to more reinsurance coverage, higher insurer profits, and lower expected distress in the industry. Journal of Economic Literature Classification Numbers: G22, G13, L15, D81.     

Does Reinsurance Need Reinsurers?

The reinsurance market is the secondary market for insurance risks. It has a very specific organization. Direct insurers rarely trade risks with each other. Rather, they cede part of their primary risks to specialized professional reinsurers who have no primary business. This article offers a model of equilibrium in reinsurance and capital markets in which professional reinsurers arise endogenously. Their role is to monitor primary insurers credibly, so that insurers can raise capital more easily. In equilibrium, the financial structure of primary insurers consists of a mix of reinsurance and outside capital. The comparative statics yield empirical predictions which are broadly in line with a number of stylized facts from the reinsurance market.     

Optimal Reciprocal Reinsurance Treaties Under the Joint Survival Probability and the Joint Profitable Probability

A reinsurance treaty involves two parties, an insurer and a reinsurer. The two parties have conflicting interests. Most existing optimal reinsurance treaties only consider the interest of one party. In this article, we consider the interests of both insurers and reinsurers and study the joint survival and profitable probabilities of insurers and reinsurers. We design the optimal reinsurance contracts that maximize the joint survival probability and the joint profitable probability. We first establish sufficient and necessary conditions for the existence of the optimal reinsurance retentions for the quota‐share reinsurance and the stop‐loss reinsurance under expected value reinsurance premium principle. We then derive sufficient conditions for the existence of the optimal reinsurance treaties in a wide class of reinsurance policies and under a general reinsurance premium principle. These conditions enable one to design optimal reinsurance contracts in different forms and under different premium principles. As applications, we design an optimal reinsurance contract in the form of a quota‐share reinsurance under the variance principle and an optimal reinsurance treaty in the form of a limited stop‐loss reinsurance under the expected value principle.     

On the economics of the longevity risk transfer market

We present a model of a longevity risk transfer market with different market players (primary insurers, reinsurers, and capital market investors) and investigate how market dynamics and the market players' roles evolve with progressing market saturation. We find that reinsurers' appetite for longevity risk is the key driver in the early stage of market development. Since diversification benefits with other businesses decrease with every transaction, the reinsurance market is intrinsically antimonopolistic. With the increasing saturation of the reinsurance sector as a whole, its competitiveness shrinks leading to rising expected risk-adjusted returns for capital market investors. We show that in a saturated market, reinsurers should assume the entire longevity risk from primary insurers, diversify it within their business mix, and subsequently pass on only specific (nondiversifiable) components of the longevity risk to the capital markets. Our findings provide valuable suggestions on how to make the best use of the market's limited risk absorption capacity.     

The market for catastrophe risk: a clinical examination

This paper examines the market for catastrophe event risk – i.e., financial claims that are linked to losses associated with natural hazards, such as hurricanes and earthquakes. Risk management theory suggests protection by insurers and other corporations against the largest cat events is most valuable. However, most insurers purchase relatively little cat reinsurance against large events, and premiums are high relative to expected losses. To understand why the theory fails, we examine transactions that look to capital markets, rather than traditional reinsurance markets, for risk-bearing capacity. We develop eight theoretical explanations and find the most compelling to be supply restrictions associated with capital market imperfections and market power exerted by traditional reinsurers.     

Optimal Risk Financing in Large Corporations through Insurance Captives

A captive is an insurance or reinsurance company established by a parent group to finance its own risks. Captives mix internal risk pooling between the business units of the parent group and risk transfer towards the reinsurance market. We analyse captives from an optimal insurance contract perspective. The paper characterises the vertical contractual chain that links firstly business units to insurance captives or to “fronters” through insurance contracts, secondly fronters to reinsurance captives through the cession of risks and thirdly insurance or reinsurance captives to reinsurers through cessions or retrocessions. In particular, the risk cession by fronters to a reinsurance captive trades off the benefits derived from recouped premiums and from the risk-sharing advantage of an “umbrella reinsurance policy”, against the risks that result from the captive liabilities.     

RELATIVE EFFICIENCIES OF NON-LIFE REINSURANCE MARKETING METHODS

Abstract: This paper extends the study of the relative cost efficiency of insurance delivery systems from the primary market to the market for non-life reinsurance services. As in the primary market for insurance services there are two predominant methods of marketing reinsurance services: reinsurers who rely on employees, termed direct writers, and those who rely on brokers.
An extensive literature relating to the primary market for non-life insurance consistently indicates that independent agency insurers have a cost disadvantage relative to exclusive agency insurers. This literature also suggests that independent agency insurers may supply superior service but a continuing erosion of the market share of independent agency insurers suggests that the perceived service differential is not valued sufficiently to offset the perceived cost differential.
The authors find evidence that, cet. par., broker supplied reinsurers operate with lower costs than direct reinsurers but we find less convincing evidence of a service differential favoring direct reinsurers. More significantly, we observe that the largest component of the traditional measure of the reinsurer's cost is the commission paid back to the primary insurer: the seemingly lower cost brokers provide a higher net cost product. Yet brokers thrive in the marketplace suggesting the existence of a product differentiated by service or quality. With the important caveat that measures of service are imperfect and data is limited, we find no evidence of a service differential.     

Regulatory capital and asset risk transfer

We 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.     

VAR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance

Abstract

It is well known that reinsurance can be an effective risk management tool for an insurer to minimize its exposure to risk. In this paper we provide further analysis on two optimal reinsurance models recently proposed by Cai and Tan. These models have several appealing features including (1) practicality in that the models could be of interest to insurers and reinsurers, (2) simplicity in that optimal solutions can be derived in many cases, and (3) integration between banks and insurance companies in that the models exploit explicitly some of the popular risk measures such as value-at-risk and conditional tail expectation. The objective of the paper is to study and analyze the optimal reinsurance designs associated with two of the most common reinsurance contracts: the quota share and the stop loss. Furthermore, as many as 17 reinsurance premium principles are investigated. This paper also highlights the critical role of the reinsurance premium principles in the sense that, depending on the chosen principles, optimal quota-share and stop-loss reinsurance may or may not exist. For some cases we formally establish the sufficient and necessary (or just sufficient) conditions for the existence of the nontrivial optimal reinsurance. Numerical examples are presented to illustrate our results.     

Keeping Some Skin in the Game: How to Start a Capital Market in Longevity Risk Transfers

The recent activity in pension buyouts and bespoke longevity swaps suggests that a significant process of aggregation of longevity exposures is under way, led by major insurers, investment banks, and buyout firms with the support of leading reinsurers. As regulatory capital charges and limited reinsurance capacity constrain the scope for market growth, there is now an opportunity for institutions that are pooling longevity exposures to issue securities that appeal to capital market investors, thereby broadening the sharing of longevity risk and increasing market capacity. For this to happen, longevity exposures need to be suitably pooled and tranched to maximize diversification benefits offered to investors and to address asymmetric information issues. We argue that a natural way for longevity risk to be transferred is through suitably designed principal-at-risk bonds.     

Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion

The quest for optimal reinsurance design has remained an interesting problem among insurers, reinsurers, and academicians. An appropriate use of reinsurance could reduce the underwriting risk of an insurer and thereby enhance its value. This paper complements the existing research on optimal reinsurance by proposing another model for the determination of the optimal reinsurance design. The problem is formulated as a constrained optimization problem with the objective of minimizing the value-at-risk of the net risk of the insurer while subjecting to a profitability constraint. The proposed optimal reinsurance model, therefore, has the advantage of exploiting the classical tradeoff between risk and reward. Under the additional assumptions that the reinsurance premium is determined by the expectation premium principle and the ceded loss function is confined to a class of increasing and convex functions, explicit solutions are derived. Depending on the risk measure's level of confidence, the safety loading for the reinsurance premium, and the expected profit guaranteed for the insurer, we establish conditions for the existence of reinsurance. When it is optimal to cede the insurer's risk, the optimal reinsurance design could be in the form of pure stop-loss reinsurance, quota-share reinsurance, or a combination of stop-loss and quota-share reinsurance.     

Risk Management, Capital Budgeting, and Capital Structure Policy for Insurers and Reinsurers

This article builds on Froot and Stein in developing a framework for analyzing the risk allocation, capital budgeting, and capital structure decisions facing insurers and reinsurers. The model incorporates three key features: (i) value‐maximizing insurers and reinsurers face product‐market as well as capital‐market imperfections that give rise to well‐founded concerns with risk management and capital allocation; (ii) some, but not all, of the risks they face can be frictionlessly hedged in the capital market; and (iii) the distribution of their cash flows may be asymmetric, which alters the demand for underwriting and hedging. We show these features result in a three‐factor model that determines the optimal pricing and allocation of risk and capital structure of the firm. This approach allows us to integrate these features into: (i) the pricing of risky investment, underwriting, reinsurance, and hedging; and (ii) the allocation of risk across all of these opportunities, and the optimal amount of surplus capital held by the firm.     

A Reexamination of the Corporate Demand for Reinsurance

This study examines the effect of the state of the international reinsurance market on the demand for reinsurance by U.S. insurers using data from the years 1993 through 2000. Both the overall demand for reinsurance and the utilization of foreign reinsurance by U.S. insurers are explored. In addition to supporting the findings of prior literature related to the traditional motives for the corporate demand for insurance, evidence indicates that the state of the U.S. reinsurance industry impacts the amount of reinsurance demanded by U.S. insurers. The study also investigates reasons why U.S. insurers utilize a reinsurance program composed of both U.S. and foreign reinsurers. The results indicate that the decision to utilize some percentage of foreign reinsurance is driven primarily by the financial and operational characteristics of the ceding company such as firm size, group affiliation, and organizational form. However, no support is found for the hypothesis that possible differences between the foreign and U.S. reinsurance markets impact the decision to utilize foreign reinsurance.     

Catastrophe Bonds,Reinsurance, and the Optimal Collateralization of Risk Transfer

Catastrophe bonds feature full collateralization of the underlying risk transfer and thus abandon the reinsurance principle of economizing on collateral through diversification of risk transfer. Our analysis demonstrates that this feature places limits on catastrophe bond penetration, even if the structure possesses frictional cost advantages over reinsurance. However, we also show that catastrophe bonds have important uses when buyers and reinsurers cannot contract over the division of assets in the event of insolvency and, more generally, cannot write contracts with a full menu of state‐contingent payments. In this environment, segregation of collateral—in the form of multiple reinsurance companies, as well as catastrophe bond vehicles—can ameliorate inefficiencies due to reinsurance contracting constraints by improving welfare for those exposed to default risk. Numerical simulation illustrates how catastrophe bonds improve efficiency in market niches with correlated risks, or with uneven exposure of buyers to reinsurer default.     

The structure of the global reinsurance market: An analysis of efficiency,scale, and scope

We estimate economies of scale and scope as well as cost and revenue efficiency to explain the structure of the global reinsurance market, where large reinsurers dominate but both diversified and specialized reinsurers are competitive. The costs and benefits of size and product diversification are particularly relevant to the reinsurance industry, as risk diversification is central to the industry's business model. We find that reinsurers with total assets less than USD 2.9 billion exhibit scale economies, while those with total assets greater than USD 15.5 billion do not. Large reinsurers are characterized by high cost efficiency, while small reinsurers exhibit superior efficiency only when specialized. Large reinsurers also exhibit revenue scope economies when operating both life and nonlife reinsurance. Moreover, the evidence is in line with the efficient structure hypothesis: cost-efficient reinsurers can charge lower prices without sacrificing profitability.     

CAT Bonds and Other Risk-Linked Securities: State of the Market and Recent Developments

This article reviews the current status of the market for catastrophic risk (CAT) bonds and other risk-linked securities. CAT bonds and other risk-linked securities are innovative financial vehicles that have an important role to play in financing mega-catastrophes and other types of losses. The vehicles are especially important because they access capital markets directly, exponentially expanding risk-bearing capacity beyond the limited capital held by insurers and reinsurers. The CAT bond market has been growing steadily, with record amounts of risk capital raised in 2005, 2006, and 2007. CAT bond premia relative to expected losses covered by the bonds have declined by more than one-third since 2001. CAT bonds now appear to be priced competitively with conventional catastrophe reinsurance and comparably rated corporate bonds. CAT bonds have grown to the extent that they now play a major role in completing the market for catastrophic-risk finance and are spreading to other lines such as automobile insurance, life insurance, and annuities. CAT bonds are not expected to replace reinsurance but to complement the reinsurance market by providing additional risk-bearing capacity. Other innovative financing mechanisms such as risk swaps, industry loss warranties, and sidecars also are expected to continue to play an important role in financing catastrophic risk.     

Leverage and reinsurance effects on loss reserves in the United Kingdom’s property–casualty insurance industry

We examine the relation between loss reserving errors, leverage and reinsurance in the UK’s property–casualty insurance industry. We find that financially weak insurers under-estimate reserves to reduce leverage, and so pre-empt costly regulatory scrutiny. However, at very high leverage, insurers over-reserve, suggesting a non-linear relation between leverage and reserving policy. We also investigate whether monitoring by reinsurers reduces reserving errors, and find that highly reinsured insurers are less likely to make loss reserve errors. However, the use of proportional reinsurance does not affect loss reserve accuracy.     

A Test of the Eclectic Paradigm: Evidence From the U.S. Reinsurance Market

This study provides a test of the eclectic paradigm with data from U.S. reinsurers. The U.S. reinsurance industry provides a unique setting to test the eclectic paradigm due to the extensive data available on U.S. reinsurers and the well‐developed literature related to reinsurance. The ability to test the hypotheses related to the eclectic paradigm in a service industry and incorporate industry‐specific factors adds to the eclectic paradigm literature which has traditionally focused primarily on manufacturing firms. In addition, the application of the eclectic paradigm to the reinsurance industry provides an empirical framework that combines several prior streams of literature which examine the reinsurer's decision to internationalize. The current study includes firm‐specific factors, country‐specific factors of the international markets, and factors related to the U.S. reinsurance industry. This article finds support for traditional factors impacting globalization such as host market size, loss experience, and competitiveness as well as reinsurer's ability to expand based on available capacity. Understanding the importance of firm‐, country‐, and industry‐specific factors is key for managers, as analyzing these issues in isolation may lead to an incomplete picture of the factors impacting the internationalization decision, hindering managers' ability to make decisions that are in the best interest of the firm. With the continued interdependence of the world reinsurance marketplace, as well as the recent expansion of the European Union, internationalization issues are of critical importance not only to U.S. insurers, reinsurers, and regulators, but also to their global counterparts.     

Participating Insurance Contracts and the Rothschild-Stiglitz Equilibrium Puzzle

We extend the Rothschild-Stiglitz (RS) insurance market model with adverse selection by allowing insurers to offer either non-participating or participating policies, that is, insurance contracts with policy dividends or supplementary calls for premium. It is shown that an equilibrium always exists in such a setting. Participating policies act as an implicit threat that dissuades deviant insurers who aim to attract low-risk individuals only. The model predicts that the mutual corporate form should be prevalent in insurance markets where second-best Pareto efficiency requires cross-subsidisation between risk types.     

Complete Versus Incomplete Insurance Contracts under Adverse Selection with Multiple Risks

This article extends the standard adverse-selection model for competitive insurance markets, which assumes a single source of risk, to the case where individuals are subject to multiple risks. We compare the following market situations—the case where insurers can offer comprehensive policies against all sources or risks (complete contracts) and the case where different risks are covered by separate policies (incomplete contracts). In the latter case, we consider whether the insurer of a particular risk has perfect information regarding an individual's coverage against other sources of risks. The analysis emphasizes the informational role of bundling in multidimensional screening. When the market situation allows bundling, it is shown that in equilibrium the low-risk type with respect to a particular source of risk does not necessarily obtain partial coverage against that particular risk.