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In this paper, we review and discuss some challenges in insuring flood risk in Europe on the national level, including high correlation of damages. Making use of recent advances in extreme value theory, we, furthermore, model flood risk with heavy-tailed distributions and their truncated counterparts and apply the discussed techniques to an inflation- and building-value-adjusted annual data set of flood losses in Europe. The analysis leads to Value-at-Risk estimates for individual countries and for Europe as a whole, allowing to quantify the diversification potential for flood risk in Europe. Finally, we identify optimal risk pooling possibilities in case a joint insurance strategy on the European level cannot be realized and quantify the resulting inefficiency in terms of additional necessary solvency capital. Thus, the results also contribute to the ongoing discussion on how public risk transfer mechanisms can supplement missing private insurance coverage.

We consider a single‐period assemble‐to‐order system that produces two types of end products to satisfy two independent and stochastic customer orders. Each type of product is used to fulfill a particular customer order and these two products share a common component. Furthermore, one customer may confirm her order before the other one, and the manufacturer needs to make a commitment immediately upon the receipt of each customer order on how many products to be delivered. We propose a model for optimizing the inventory and production decisions under the above ATO environment. We also extend our model to the situation where the manufacturer can fulfill the unsatisfied low‐priority demand using the left‐over inventories after fulfilling the high‐priority demand, in case the low‐priority customer arrives first. Numerical experiments are conducted, which provide some interesting insights on the impact of uncertain demand pattern.

Background Despite sophisticated risk equalization, insurers in regulated health insurance markets still face incentives to attract healthy people and avoid the chronically ill because of predictable differences in profitability between these groups. The traditional approach to mitigate such incentives for risk selection is to improve the risk-equalization model by adding or refining risk adjusters. However, not all potential risk adjusters are appropriate. One example are risk adjusters based on health survey information. Despite its predictiveness of future healthcare spending, such information is generally considered inappropriate for risk equalization, due to feasibility challenges and a potential lack of representativeness. Methods We study the effects of high-risk pooling (HRP) as a strategy for mitigating risk selection incentives in the presence of sophisticated– though imperfect– risk equalization. We simulate a HRP modality in which insurers can ex-ante assign predictably unprofitable individuals to a ‘high risk pool’ using information from a health survey. We evaluate the effect of five alternative pool sizes based on predicted residual spending post risk equalization on insurers’ incentives for risk selection and cost control, and compare this to the situation without HRP. Results The results show that HRP based on health survey information can substantially reduce risk selection incentives. For example, eliminating the undercompensation for the top-1% with the highest predicted residual spending reduces selection incentives against the total group with a chronic disease (60% of the population) by approximately 25%. Overall, the selection incentives gradually decrease with a larger pool size. The largest marginal reduction is found moving from no high-risk pool to HRP for the top 1% individuals with the highest predicted residual spending. Conclusion Our main conclusion is that HRP has the potential to considerably reduce remaining risk selection incentives at the expense of a relatively small reduction of incentives for cost control. The extent to which this can be achieved, however, depends on the design of the high-risk pool.

The decision of a firm to set up a plant network is influenced by a number of factors, including demand fluctuations across its portfolio of products, logistics costs, and service level requirements. Product plant networks offer the benefits of consolidated production and reduced transshipment costs; on the other hand, process plant networks allow intensive dedication to process expertise and economies of scale. In this paper, we show that, aside from these benefits, process plant networks offer significant risk pooling advantages under a wide range of conditions. We analytically demonstrate that, even without accounting for economies of scale advantages, firms may prefer the process plant network configuration due to the risk pooling benefits offered.

This report addresses the large flood exposures of Central Europe and proposes efficient financial and risk transfer mechanisms to mitigate fiscal losses from natural catastrophes. In particular, the Visegrad countries (V-4) of Central Europe, namely, Poland, the Czech Republic, Hungary, and the Slovak Republic, have such tremendous potential flood damages that reliance on budgetary appropriations or even European Union (EU) funds in such circumstances becomes ineffective and does not provide needed cash funds for the quick response and recovery needed to minimize economic disruptions. The report is primarily addressed to the governments of the region, which should build into their fiscal planning the necessary contingent funding mechanisms, based on their exposures. The report is addressed to finance ministries and also to the insurance and securities regulators and the private insurance and capital markets, which may all play a role in the proposed mechanisms. An arrangement using a multi-country pool with a hazard-triggered insurance payout mechanism complemented by contingent financing is proposed, to better manage these risks and avoid major fiscal volatility and disruption.

The interdependency of information security risks often induces firms to invest inefficiently in information technology security management. Cyberinsurance has been proposed as a promising solution to help firms optimize security spending. However, cyberinsurance is ineffective in addressing the investment inefficiency caused by risk interdependency. In this paper, we examine two alternative risk management approaches: risk pooling arrangements (RPAs) and managed security services (MSSs). We show that firms can use an RPA as a complement to cyberinsurance to address the overinvestment issue caused by negative externalities of security investments; however, the adoption of an RPA is not incentive-compatible for firms when the security investments generate positive externalities. We then show that the MSS provider serving multiple firms can internalize the externalities of security investments and mitigate the security investment inefficiency. As a result of risk interdependency, collective outsourcing arises as an equilibrium only when the total number of firms is small.

Using risk-reducing properties of conditional expectations with respect to convex order, Denuit and Dhaene [Denuit, M. and Dhaene, J. (2012). Insurance: Mathematics and Economics 51, 265–270] proposed the conditional mean risk sharing rule to allocate the total risk among participants to an insurance pool. This paper relates the conditional mean risk sharing rule to the size-biased transform when pooled risks are independent. A representation formula is first derived for the conditional expectation of an individual risk given the aggregate loss. This formula is then exploited to obtain explicit expressions for the contributions to the pool when losses are modeled by compound Poisson sums, compound Negative Binomial sums, and compound Binomial sums, to which Panjer recursion applies. Simple formulas are obtained when claim severities are homogeneous. A couple of applications are considered: first, to a peer-to-peer insurance scheme where participants share the first layer of their respective risks while the higher layer is ceded to a (re)insurer; second, to survivor credits to be shared among surviving participants in tontine schemes.

We consider a one-warehouse, N-retailer, multiperiod, stock allocation problem in which holding costs are identical at each location and no stock is received from outside suppliers for the duration of the planning horizon. No shipments are allowed between retailers. The only motive for holding inventory at the central warehouse for allocation in future periods is the so-called risk pooling motive. We apply robust optimization to this problem extending the inventory policy to allow for an adaptive, nonanticipatory shipment policy. We consider two alternatives for the uncertainty set, one in which risk pooling is implicit and another for which risk pooling is explicit. The explicit risk pooling uncertainty set grows by no more than the square of the number of retailers. The general problem can be solved using Benders’ decomposition. A special case gives rise to closed-form solutions for both uncertainty set alternatives. The explicit risk pooling uncertainty set leads to a square root law in which the optimal stock to reserve at the central warehouse grows with the square root of the number of retailers. The experimental results confirm the value of the robust optimization approach and provide managerial insights into the operation of such systems. This paper was accepted by Yinyu Ye, optimization.

Survivor funds are financial arrangements where participants agree to share the proceeds of a collective investment pool in a predescribed way depending on their survival. This offers investors a way to benefit from mortality credits, boosting financial returns. Following Denuit (2019, ASTIN Bulletin, 49, 591–617), participants are assumed to adopt the conditional mean risk sharing rule introduced in Denuit and Dhaene (2012, Insurance: Mathematics and Economics, 51, 265–270) to assess their respective shares in mortality credits. This paper looks at pools of individuals that are heterogeneous in terms of their survival probability and their contributions. Imposing mild conditions, we show that individual risk can be fully diversified if the size of the group tends to infinity. For large groups, we derive simple, hierarchical approximations of the conditional mean risk sharing rule.

Using an agent-based model to study risk-pooling in herder dyads using rules derived from Maasai osotua (\"umbilical cord\") relationships, Aktipis et al. (2011) found that osotua transfers led to more risk-pooling and better herd survival than both no transfers and transfers that occurred at frequencies tied to those seen in the osotua simulations. Here we expand this approach by comparing osotua-style transfers to another type of livestock transfer among Maasai known as esile (\"debt\"). In osotua, one asks if in need, and one gives in response to such requests if doing so will not threaten one's own survival. In esile relationships, accounts are kept and debts must be repaid. We refer to these as \"need-based\" and \"account-keeping\" systems, respectively. Need-based transfers lead to more risk pooling and higher survival than account keeping. Need-based transfers also lead to greater wealth equality and are game theoretically dominant to account-keeping rules.