Risk-sharing Rules Research Articles

Risk sharing and information revelation mechanism of a one-manufacturer and one-retailer supply chain facing an integrated competitor

This paper develops an information revelation mechanism model of a one-manufacturer and one-retailer supply chain facing an outside integrated-competitor under demand uncertainty. We investigate how the manufacturer designs a wholesale price-order quantity contract to induce the retailer to report his risk sensitivity information truthfully. We try to explore the effects of the outside competitor and the risk-sharing rule on the optimal price-service level decisions of the retailer and the optimal wholesale prices of the manufacturer. We find that the strategic interaction plays an important role in the effect of risk sensitivity on the order quantity for the retailer. When the fraction of the risk cost shared by the manufacturer is sufficiently large (small), the optimal wholesale price for the high risk-averse retailer is higher (lower) than that for the low risk-averse retailer.

Voting over Informal Risk-Sharing Rules

People vote over risk-sharing rules to cope with random revenues. Risk-sharing rules are enforced through peer pressure: those who comply exert a negative externality on those who do not. People are difierently afiected by this externality. I determine the elected risk-sharing rules and the level of compliance. It turns out that full risk-sharing is achieved only if everybody complies . Partial risk-sharing is more often achieved with, sometime, some level of non-compliance. In many cases, a majority of people votes over and complies with the risk-sharing rule that maximizes their own expected payofi.

Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities

Efficient risk-sharing rules and equilibria between two agents with utilities in a class that contains the rank dependent expected utility (RDU) are fully characterized. Specific attention is given to the RDU. Call-spreads and contracts with mixed regimes are shown to be efficient. Closed-form solutions are obtained for several examples.

Representative consumer's risk aversion and efficient risk-sharing rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.

HETEROGENEOUS RISK ATTITUDES IN A CONTINUOUS-TIME MODEL*

We prove that every continuous-time model in which all consumers have time-homogeneous and time-additive utility functions and share a common probabilistic belief and a common discount rate can be reduced to a static model. This result allows us to extend some of the existing results of the representative consumer and risk-sharing rules in static models to continuous-time models. We show that the equilibrium interest rate is lower and more volatile than in the standard representative consumer economy, and that the individual consumption growth rates are more dispersed than in the absence of uncertainty.

Efficient Risk-Sharing Rules with Heterogeneous Risk Attitudes and Background Risks

In an exchange economy in which there is a complete set of markets for macroeconomic risks but no market for idiosyncratic risks, we consider how the efficient risk-sharing rules for the macroeconomic risk are affected by the heterogeneity in the consumers' risk attitudes and idiosyncratic risks. We provide sufficient conditions under which an idiosyncratic risk increases cautiousness (the derivative of the reciprocal of the absolute risk aversion), the determinant of the curvatures of the efficient risk-sharing rules. While the curvature of the risk-sharing rules at high consumption levels are governed by the consumers' risk attitudes, the curvature at low consumption levels depend not only on the risk attitudes but also on the lower tail distributions of the idiosyncratic risks.

Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.

Who should control inventory in a supply chain?

In view of the recent popularity in supply chain management to transfer the stock level decision and the stock keeping responsibility to the upstream, we consider in this paper whether a two-member supply chain (the upstream vendor V and the downstream retailer R) operating in a newsboy environment should adopt this new mechanism. The supply chain can be operated in one of two ways: the traditional way, in which the downstream retailer decides the inventory level and keeps the inventory, or the new way in which inventory-keeping responsibility and stock level decision switch to the upstream vendor. By comparing the expected payoffs in these two cases, we find that transferring demand-uncertainty risk from R to V does not necessarily lead to a higher expected payoff for R or a lower one for V. In general, we find that the critical fractile used in a newsboy problem to determine the optimal stock level can often be used as a yardstick to quickly assess the merits of adopting the new mechanism. Furthermore, we show that when the critical fractile of V is greater than that of R, adopting the new mechanism always makes both V and R better off, provided some kind of risk-sharing rule could be implemented.

OPERATING LEVERAGE AND THE INTERACTION BETWEEN ABANDONMENT OPTIONS AND EXOTIC HEDGING

This paper examines the interaction between operational and financial hedging in the context of the competitive firm under output price uncertainty. The firm is endowed with an abandonment option in that its production decision is made after the true realization of the random output price has been observed. If the realized output price is less than its marginal cost, the firm optimally exercises its abandonment option and ceases from production. Otherwise, the firm lets its abandonment option extinguish and produces at its capacity. The existence of the abandonment option is shown to induce the firm to opt for a concave payoff risk-sharing rule that can be perfectly replicated by writing call options with a single strike price set equal to the marginal cost. We derive necessary and sufficient conditions that ensure a positive (negative) effect of operational hedging via the abandonment option on the firm's optimal operating leverage. In contrast, we show that the effect of financial hedging via customized exotic derivatives on the firm's optimal operating leverage is unambiguously positive. These results suggest that the interaction between abandonment options and exotic hedging is multi-dimensional and deserves further scrutiny.

Relationships Between Risk Aversion, Prudence and Cautiousness

In this paper we investigate the relationships between risk aversion, prudence, and cautiousness, which have interpretations for investors' behaviour in different financial activities. We show if an investor is always more prudent then she is almost always more risk averse. Assuming investors' marginal utility of zero wealth is infinity, we show when an investor's wealth approaches zero or infinity, in limit cautiousness equals the inverse of relative risk aversion, if an investor's cautiousness is bounded from above (below) by a positive constant then his relative risk aversion is bounded below (above) by the inverse of the constant, and an investor who always has higher cautiousness is always less relative risk averse along her optimal risk-sharing rule in an economy. We also show that increasing (decreasing) cautiousness implies decreasing (increasing) relative risk aversion.

Optimal risk-sharing rules and equilibria with Choquet-expected-utility

This paper explores risk-sharing and equilibrium in a general equilibrium set-up wherein agents are non-additive expected utility maximizers. We show that when agents have the same convex capacity, the set of Pareto-optima is independent of it and identical to the set of optima of an economy in which agents are expected utility maximizers and have the same probability. Hence, optimal allocations are comonotone. This enables us to study the equilibrium set. When agents have different capacities, the matters are much more complex (as in the vNM case). We give a general characterization and show how it simplifies when Pareto-optima are comonotone. We use this result to characterize Pareto-optima when agents have capacities that are the convex transform of some probability distribution. Comonotonicity of Pareto-optima is also shown to be true in the two-state case if the intersection of the core of agents' capacities is non-empty; Pareto-optima may then be fully characterized in the two-agent, two-state case. This comonotonicity result does not generalize to more than two states as we show with a counter-example. Finally, if there is no-aggregate risk, we show that non-empty core intersection is enough to guarantee that optimal allocations are full-insurance allocation. This result does not require convexity of preferences.

Construction Joint Ventures

A construction joint venture is a partnership of contractors who have formed a business alliance for the purpose of undertaking a project. Motivation for such an alliance may be technological complexity, political expediancy, large size, or high risk. An analysis of the risk-sharing characteristics is presented concentrating on principles of diversification for the individual contractors and competitive advantage of the joint venture as a whole. A formulation of risk-sharing rules and basic contractor risk behavioral criteria leads to the development of a methodology for optimal joint-venture share allocation. By means of a three contractor joint-venture example the optimal allocation of shares is demonstrated, as well as a verification of principles of diversification and competitive advantage.

Impossibility and Related Doctrines in Contract Law: An Economic Analysis

… The typical case in which impossibility or some related doctrine is invoked is one where, by reason of an unforeseen or at least unprovided-for event, performance by one of the parties of his obligations under the contract has become so much more costly than he foresaw at the time the contract was made as to be uneconomical (that is, the costs of performance would be greater than the benefits). The performance promised may have been delivery of a particular cargo by a specified delivery date – but the ship is trapped in the Suez Canal because of a war between Israel and Egypt. Or it may have been a piano recital by Gina Bachauer – and she dies between the signing of the contract and the date of the recital. The law could in each case treat the failure to perform as a breach of contract, thereby in effect assigning to the promisor the risk that war, or death, would prevent performance (or render it uneconomical). Alternatively, invoking impossibility or some related notion, the law could treat the failure to perform as excusable and discharge the contract, thereby in effect assigning the risk to the promisee. From the standpoint of economics – and disregarding, but only momentarily, administrative costs – discharge should be allowed where the promisee is the superior risk bearer; if the promisor is the superior risk bearer, nonperformance should be treated as a breach of contract. “Superior risk bearer” is to be understood here as the party that is the more efficient bearer of the particular risk in question, in the particular circumstances of the transaction.