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The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets of risk measures. This study extends the inf-convolution of risk measures in its convex-combination form to a countable (not necessarily finite) set of alternatives. The intuitive meaning of this approach is to represent a generalization of the current finite convex weights to the countable case. Subsequently, we extensively generalize known properties and results to this framework. Specifically, we investigate the preservation of properties, dual representations, optimal allocations, and self-convolution. [ABSTRACT FROM AUTHOR]

With the rise of decentralized finance and insurance technology, there has been growing interest in the financial industry for risk sharing mechanisms without a central authority or clearing house. In contrast with classic centralized risk sharing, a novel peer-to-peer risk sharing framework is proposed. The presented framework aims to devise a risk allocation mechanism that is structurally decentralized, Pareto optimal, and mathematically fair. An explicit form for the pool allocation ratio matrix is derived, and convex programming techniques are applied to determine the optimal pooling mechanism in a constrained variance reduction setting. A tiered hierarchical generalization is also constructed to improve computational efficiency. As an illustration, these techniques are applied to a flood risk pooling example. Flood risk is known to be difficult to cover in practice, which contributes to the stagnant development for a private insurance market. It is shown in this paper that peer-to-peer risk sharing techniques provide an economically viable alternative to traditional flood insurance policies. [ABSTRACT FROM AUTHOR]

The need to obtain financial funds to pursue public utility investments implies the generation of Public-Private Partnership (PPP) projects. The PPP framework can involve risk-sharing mechanisms between public administration and private sector to encourage private investors to fund these projects. However, these risk-sharing mechanisms, such as Minimum Revenue Guarantee or Revenue Cap (RC), could generate opportunistic behaviors. For this reason, we can set this problem as a game in which government and private investors would act as players. This paper proposes a mathematical model to evaluate the PPP projects through a combination of Game Theory (GT) and Real Options Approach (ROA). The ROA is needed to price the uncertainty that affects PPP investments, and the GT captures the strategic interactions between public and private sectors. A case study on a wastewater treatment project is developed to apply the model we proposed. [ABSTRACT FROM AUTHOR]

We model the optimal choice of the contract terms of a foreign exchange risk sharing supply contract between a buyer and supplier who are located in two different countries, when the supplier quotes a wholesale price in its currency, and both parties are mean variance expected utility maximizers. We extend the model to examine alternatives to the risk sharing contract, which are the wholesale price contract without risk hedging and a wholesale price contract with transfer of risk by the buyer to an options dealer. We empirically apply the model, to two different currencies of the supplier, by assuming that the buyer is based in the U.S., while the supplier is based in one of two countries, which are Switzerland and the U.K. Our results show that the performance of the risk sharing contract provides a substantial improvement in the total expected utility of both partners to the contract, over both the wholesale price contract without risk hedging and the risk transfer contract. [ABSTRACT FROM AUTHOR]

This work presents an original proposal for the reform of the Eurozone architecture according to an approach based on risk sharing (aiming to reach in the long-term the mutualization of public debt). The proposal envisages a new role for the European Stability Mechanism (ESM) which should gradually become the guarantor of the public debts of the European Economic and Monetary Union (EMU). In this way, the new ESM would support the full transition from national debts to a single Eurozone public debt (e.g. Eurobonds) with a single yield curve for all countries. Our proposal would benefit both core and peripheral EMU countries. Indeed, the riskiest countries, which would gain from the ESM conditional debt guarantee, should give up the possibility of redenominating their national debt and would pay to the ESM the corresponding market price of the guarantee. This would strengthen the capital endowment of the ESM and also allow it to use its leverage capability to support the realignment of the economic cycles of the different countries through profitable public investment plans concentrated in the weakest regions of the EMU. Such plans would be coordinated and implemented by the European Union. After a transition period, our Insurance Fund proposal would contribute to a much more resilient monetary union, with a European fiscal policy and mutualized debt. Admittedly this proposal presupposes a political consensus at the EU level to reinterpret the no bailout rule enshrined in the treaties so that risk sharing institutions implemented with fairly priced insurance scheme can be allowed. New risk sharing institutions will foster a common vision of belonging to the same federal, political union in the making, the only one compatible with the abdication of fiscal sovereignty by national governments. [ABSTRACT FROM AUTHOR]

The notion of Pareto optimality is commonly employed to formulate decisions that reconcile the conflicting interests of multiple agents with possibly different risk preferences. In the context of a one-period reinsurance market comprising an insurer and a reinsurer, both of which perceive risk via distortion risk measures, also known as dual utilities, this article characterizes the set of Pareto-optimal reinsurance policies analytically and visualizes the insurer-reinsurer trade-off structure geometrically. The search of these policies is tackled by translating it mathematically into a functional minimization problem involving a weighted average of the insurer's risk and the reinsurer's risk. The resulting solutions not only cast light on the structure of the Pareto-optimal contracts, but also allow us to portray the resulting insurer-reinsurer Pareto frontier graphically. In addition to providing a pictorial manifestation of the compromise reached between the insurer and reinsurer, an enormous merit of developing the Pareto frontier is the considerable ease with which Pareto-optimal reinsurance policies can be constructed even in the presence of the insurer's and reinsurer's individual risk constraints. A strikingly simple graphical search of these constrained policies is performed in the special cases of Value-at-Risk and Tail Value-at-Risk. [ABSTRACT FROM AUTHOR]

In the paper, we study the inventory centralization problem with risk-averse newsvendors using cooperative game theory. Pareto-optimality and collective rationality conditions are adopted to characterize the stable profit allocations among coalition members. Pareto-optimal profit allocation rules are derived for exponential and power utilities while the necessary and sufficient conditions are shown for stable profit allocations. We also show that the game model has a nonempty core when the exponential and power utilities are adopted to describe the risk-averse behavior. [ABSTRACT FROM AUTHOR]

Developing an efficient policy to determine the inventory a non-profit organization (NPO) should stockpile to respond to potential disasters plays a vital role in humanitarian relief. Incorporating social donation and emergency spot purchasing, this paper develops a (generalized) two-stage delivery process model to characterize relief materials' delivery after a disaster. We propose an analytical model that aims to minimize the total costs when all demands incurred by an unexpected disaster need to be fully satisfied. Moreover, we determine that the optimal solution uniquely exists and characterize the effects of key parameters. Last, this paper also develops a risk-sharing scheme, in which the NPO and the supplier jointly stockpile relief materials. Under some mild conditions, we show that implementing the scheme could increase the storage quantity and decrease the total costs simultaneously. Several numerical examples are employed to validate the model, as well as the value of the proposed risk-sharing scheme. [ABSTRACT FROM AUTHOR]

Cooperative investment consists of two problems: finding an optimal cooperative investment strategy and fairly dividing investment outcome among participating agents. In general, the two problems cannot be solved separately. It is known that when agents' preferences are represented by mean-deviation functionals, sharing of optimal portfolio creates instruments that, on the one hand, satisfy individual risk preferences but, on the other hand, are not replicable on an incomplete market, so that each agent is strictly better off in participating in cooperative investment than investing alone. This synergy effect is shown to hold when agents' acceptance sets are represented by cash-invariant utility functions in the case of multiperiod investment with an arbitrary feasible investment set. In this case, a set of all Pareto-optimal allocations is characterized, and an equilibrium-based method for selecting a 'fair' Pareto-optimal allocation is suggested. It is also shown that if exists, the 'fair' allocation belongs to the core of the corresponding cooperative game. The equilibrium-based method is then extended to the case of arbitrary utility functions. The obtained results are demonstrated in a multiperiod cooperative investment problem with investors imposing drawdown constraints on investment strategies. [ABSTRACT FROM AUTHOR]

An optimal risk sharing problem for agents with utility functionals depending only on the expected value and a deviation measure of an uncertain payoff has been studied. The agents are assumed to have no initial endowments. A set of Pareto-optimal solutions to the problem has been characterized, and a particular solution from the set has been suggested. If an equilibrium exists, the suggested solution coincides with an equilibrium solution. As special cases, the optimal risk sharing problem in the form of expected gain maximization and the problem with a linear mean-deviation utility functional including averse and coherent risk measures have been addressed. In the case of expected gain maximization, the existence of an equilibrium has been shown. [ABSTRACT FROM AUTHOR]