Dynamic risk-sharing game and reinsurance contract design

This paper studies the optimal risk-sharing between an insurer and a reinsurer. The insurer purchases reinsurance for risk-control and decides her retention level with an objective to minimize her ruin probability. The reinsurer has control over the reinsurance price and aims to maximize her expected discounted profits up to the time when the insurer goes bankrupt. In a stochastic differential game-theoretic framework, we determine the insurer’s optimal reinsurance strategy and specify the reinsurance contract by solving a system of coupled Hamilton–Jacobi–Bellman equations. We obtain explicit solutions for the game problem when both the insurance and the reinsurance premiums are calculated according to the standard-deviation principle or the expected value principle, respectively. Our results show that, depending on the model parameters, the reinsurance contract is either provided with a peak price when the insurer has sufficient cash reserve and with a minimum price when otherwise, or is always provided with a peak price. We also perform some numerical analyses and provide economic interpretations for the results.     

Optimal risk-sharing under mutually singular beliefs

We focus on the situation in which agents might have mutually singular beliefs in a maxmin expected utility framework. We show the existence of an equilibrium under fairly general conditions. We further demonstrate that the characterization of Pareto optimal allocation is significantly different from the classical situation, where all beliefs are mutually equivalent for each agent. Absent aggregate uncertainty, we prove that with common beliefs among agents, any Pareto optimal allocation is a full insurance under the upper capacities for all agents. But the full insurance feature of all Pareto optimal allocations, if true, does not necessarily ensure common beliefs. Moreover, despite agents have sharing beliefs, a full insurance Pareto optimal allocation could be associated with intricate allocation form.     

Optimal risk-sharing across a network of insurance companies

Risk transfer is a key risk and capital management tool for insurance companies. Transferring risk between insurers is used to mitigate risk and manage capital requirements. We investigate risk transfer in the context of a network environment of insurers and consider capital costs and capital constraints at the level of individual insurance companies. We demonstrate that the optimisation of profitability across the network can be achieved through risk transfer. Considering only individual insurance companies, there is no unique optimal solution and, a priori, it is not clear which solutions are fair. However, from a network perspective, we derive a unique fair solution in the sense of cooperative game theory. Implications for systemic risk are briefly discussed.     

The effect of market power on risk-sharing

The paper studies an oligopolistic equilibrium model of financial agents who aim to share their random endowments. The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent’s set of strategic choices consists of the security payoffs and the pricing kernel that are consistent with the optimal-sharing rules; while in the incomplete setting, agents respond via demand functions on a vector of given tradeable securities. It is shown that at the (Nash) risk-sharing equilibrium, the sharing securities are suboptimal, since agents submit for sharing different risk exposures than their true endowments. On the other hand, the Nash equilibrium prices stay unaffected by the game only in the special case of agents with the same risk aversion. In addition, agents with sufficiently lower risk aversion act as predatory traders, since they absorb utility surplus from the high risk averse agents and reduce the efficiency of sharing. The main results of the paper also hold under the generalized models that allow the presence of noise traders and heterogeneity in agents’ beliefs.     

Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan

A continuous time stochastic model is used to study a hybrid pension plan, where both the contribution and benefit levels are adjusted depending on the performance of the plan, with risk sharing between different generations. The pension fund is invested in a risk-free asset and multiple risky assets. The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan trustees and participants so that this proposed hybrid pension system provides adequate and stable income to retirees while adjusting contributions effectively, as well as keeping its sustainability in the long run. These goals are achieved by minimizing the expected discount disutility of intermediate adjustment for both benefits and contributions and that of terminal wealth in finite time horizon. Using the stochastic optimal control approach, closed-form solutions are derived under quadratic loss function and exponential loss function. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions. Through numerical analysis, we find that the optimal strategies do adjust the contributions and retirement benefits according to fund performance and model objectives so the intergenerational risk sharing seem effectively achieved for this collective hybrid pension plan.     

Qualitative criteria of admissibility for enforced agreements

It is desirable that artificial agents can help each other when they cannot achieve their goals, or when they profit from social exchanges. In this work we study coalition formation processes supported by enforced agreements and we define two qualitative criteria, the do-ut-des property and the composition property, that establish when a coalition is admissible to be formed. The do-ut-des property is based on a balance between the advantages and the burdens of an agent, when it agrees an enforced agreements. The composition property is a refinement of the do-ut-des property that takes into account also the costs and the risks deriving from the coalition formation process. Two relevant aspects distinguish our approach from the solution criteria developed in cooperative game theory. First, the do-ut-des property and the composition property are not based on an explicit utility function associated to the goals of an agent, and hance they can be used also in that cases in which the importance that agents give to their own goals is unknown. Second, a coalition has all the necessary information to establish if it satisfies the do-ut-des property or the composition property, therefore these two properties can be used in the case not all the space of possible coalitions is known. Luigi Sauro graduated in Physics at the University “Federico II” of Naples in 2001. From February 2002 to July 2002 he was collaborator at the SRA division of the IRST Institute (Trento). He got is Ph.D. in Computer Science from University of Torino in February 2006. Currently he is member of the Natural Language Processing and Agents Group, directed by prof. Leonardo Lesmo. His research interests include social reasoning, coalition formation and coordination in multiagent systems.     

Non-binding agreements and fairness in commons dilemma games

Usually, common pool games are analyzed without taking into account the cooperative features of the game, even when communication and non-binding agreements are involved. Whereas equilibria are inefficient, negotiations may induce some cooperation and may enhance efficiency. In the paper, we propose to use tools of cooperative game theory to advance the understanding of results in dilemma situations that allow for communication. By doing so, we present a short review of earlier experimental evidence given by Hackett, Schlager, and Walker 1994 (HSW) for the conditional stability of non-binding agreements established in face-to-face multilateral negotiations. For an experimental test, we reanalyze the HSW data set in a game-theoretical analysis of cooperative versions of social dilemma games. The results of cooperative game theory that are most important for the application are explained and interpreted with respect to their meaning for negotiation behavior. Then, theorems are discussed that cooperative social dilemma games are clear (alpha- and beta-values coincide) and that they are convex (it follows that the core is “large”): The main focus is on how arguments of power and fairness can be based on the structure of the game. A second item is how fairness and stability properties of a negotiated (non-binding) agreement can be judged. The use of cheap talk in evaluating experiments reveals that besides the relation of non-cooperative and cooperative solutions, say of equilibria and core, the relation of alpha-, beta- and gamma-values are of importance for the availability of attractive solutions and the stability of the such agreements. In the special case of the HSW scenario, the game shows properties favorable for stable and efficient solutions. Nevertheless, the realized agreements are less efficient than expected. The realized (and stable) agreements can be located between the equilibrium, the egalitarian solution and some fairness solutions. In order to represent the extent to which the subjects obey efficiency and fairness, we present and discuss patterns of the corresponding excess vectors.     

Managing a portfolio of long term service agreements

Long-term service agreements (LTSAs) for the maintenance of capital-intensive equipments such as gas turbines and aircraft engines are gaining wide acceptance. A typical LTSA contract spans over a period of around 10 years making a manufacturer fully responsible for maintaining the customer equipment. In this paper, we address the management of a portfolio of such contracts from the manufacturer’s perspective. The goal is to meet all the service requirements imposed by the contracts while minimizing total cost incurred. We develop a deterministic integer programming model to generate the optimal maintenance schedules that minimize the total portfolio cost. We then propose two heuristic algorithms for the problem.     

Negotiation,preferences over agreements,and the core

We analyze conditions under which negotiated agreements are efficient from the point of view of every possible coalition of negotiators. The negotiators have lexicographic preferences over agreements they reach. Their utility is the first criterion. The coalition reaching an agreement is the second criterion. In the analyzed non-cooperative discrete time bargaining game Γ the players bargain about the choice from the sets of utility vectors feasible for coalitions in a given NTU game (N, V). If Γ has a Markov perfect equilibrium, then the set of equilibrium utility vectors in Markov perfect equilibria in it equals the core of (N, V). I thank an anonymous referee, an anonymous Associate Editor, and the Editor for their comments that helped me to improve the paper. The research reported in this paper was supported by the Grant VEGA 1/1223/04 of the Ministry of Education of the Slovak Republic.     

A new method for valuing underwriting agreements for rights issues

The problem of valuing underwriting agreements for rights issues is addressed. In the recent literature the theory of put options has been used to find the premiums for these services. It has been a puzzle to date that the values obtained by this method have not been in agreement with observed premiums paid by the firms to the underwriters. In particular, one has concluded that firms have overpaid for underwriting. In this paper we use the theory of contingent claims analysis to find an equation on which the premium computation must be based. We derive an upper and a lower bound for the net premium, and we compare the values obtained by our method to the premiums computed by the traditional technique for 22 rights issues listed on the stock exchange in Oslo (Oslo Børs). It turns out that in many cases the discrepancies between the two methods can be substantial. In particular, from the upper bounds and from the risk-adjusted probabilities that the issues are successful, we infer that the traditional technique may sometimes undervalue these premiums. Thus we argue that the market for underwriting agreements is not inefficient after all.     

Scoring rule and majority agreements for large electorates with arbitrary preferences

This paper examines elections among three candidates when the electorate is large and voters can have any of the 26 nontrivial asymmetric binary relations on the candidates as their preference relations. Comparisons are made between rule-λ rankings based on rank-order ballots and simple majorities based on the preference relations. The rule-λ ranking is the decreasing point total order obtained when 1, λ and 0 points are assigned to the candidates ranked first, second and third on each voter's ballot, with 0 ? λ ? 1.Limit probabilities as the number of voters gets large are computed for events such as ‘the first-ranked rule-λ candidate has a majority over the second-ranked rule-λ candidate’ and ‘the rule-λ winner is the Condorcet candidate, given that there is a Condorcet candidate’. The probabilities are expressed as functions of λ and the distribution of voters over types of preference relations. In general, they are maximized at λ = 1/2 (Borda) and minimized at λ = 0 (plurality) and at λ = 1 for any fixed distribution of voters over preference types. The effects of more indifference and increased intransitivity in voter's preference relations are analyzed when λ is fixed.     

Sticks and carrots for the design of international climate agreements with renegotiations

This paper examines renegotiations of international climate agreements for carbon abatement. We explore coalition stability under ‘optimal transfers’ that have been suggested to stabilise international environmental agreements (e.g. McGinty in Oxford Economic Papers 59, 45–62, 2007). Such transfer schemes need to be refined when agreements are renegotiated. We determine the requirements that transfers between signatories of an international climate agreement must satisfy in order to stabilise the sequence of agreements that performs best in terms of provision of the public good ‘carbon abatement’. If these requirements are met, no country wants to change its membership status at any stage. In order to demonstrate the applicability of our result we use the STACO model, a 12-regions global model, to assess the impact of well-designed transfer rules on the stability of an international climate agreement. Although there are strong free-rider incentives, we find a stable grand coalition in the first commitment period in a game with one round of renegotiations if renegotations take place sufficiently early.     

An extension of inventory models incorporating financing agreements with both suppliers and customers

In a recent article, Min et al. [J. Min, Y.W. Zhou, J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Appl. Math. Model. 34 (2010) 3273–3285] presented an inventory model for a retailer with inventory-level-dependent demand as well as upstream and downstream financing agreements. The purpose of this note is twofold: (1) to relax the boundary condition imposed in their model that ensures the entire stock is depleted at the end of each order cycle and (2) to resolve the potential unbounded solution resulting from a linear demand function by constraining the maximum inventory level. The effects of these changes on the retailer’s profitability are examined and some practical generalizations of the model are presented.     

Evaluation of rankings with regard to the possible number of agreements and conflicts

An interesting problem in group decision analysis is how many different agreements can occur, or conversely disagreements may exist, between two or more different rankings of a set of alternatives. In this paper it is assumed that a reference ranking has been established for the set of alternatives. This reference ranking may represent the ranking of a high authority decision maker or be just a virtual ranking to be used in determining the discrepancy between pairs of rankings. Then, the problem examined here is to evaluate the number of possible rankings when the ranking method is the number of agreements with some reference ranking. The analysis presented here illustrates that this problem is not trivial and moreover, its simple context conceals complexity in its depth. The purpose of this paper is to provide an evaluation of the number of possible agreements in rankings given to a set of concepts, alternatives or ideas, by two or more decision makers. The number of possible agreements takes on the values 0, 1, 2,…, n − 2, or n when n concepts are compared. This paper develops a recursive closed form formula for calculating the frequencies for the various numbers of agreements.     

Thin film tribology of pharmaceutical elastomeric seals

The primary purpose of valve seals in inhalation and other drug dispensing devices is to inhibit leakage of highly volatile formulation from pressurised canisters. This requirement often conflicts with smooth operation of valves because of poor lubrication of seals. The repercussions of this can be variability in dispensed dose as well as loss of prime and gradual wear of seals. Although a good volume of literature is available for general purpose o-ring seals, the characteristic behaviour of those used in pharmaceutical devices deviate from this significantly. The paper studies tribology of such seals, subjected to global fitment and canister pressure deformation and localised conjunctional elastohydrodynamic pressures. It is shown that ideally smooth seals would operate under iso-viscous elastic (soft EHL) regime of lubrication. However, the predicted ultra-thin films are insufficient to ensure fluid film lubrication because of rough micro-scale nature of elastomeric seal surface and poor lubricity of the usual bio-compatible formulations. The paper also shows that siliconisation of elastomeric contacting surface only marginally improves its tribological performance.     

Robust distribution planning for supplier-managed inventory agreements when demand rates and travel times are stationary

Supplier-managed inventory (SMI) is a partnering agreement between a supplier and his customers. Under this SMI agreement, inventory monitoring and ordering responsibilities are entirely transferred to the supplier. Subsequently, the supplier decides both the quantity and timing of his customer deliveries. The inventory routing problem is an underlying optimization model for SMI partnerships to cost-effectively coordinate and manage customer inventories and related replenishments logistics. This paper discusses the case where customer demand rates and travel times are stochastic but stationary, and proposes a version of the inventory routing optimization model that generates optimal robust distribution plans. The approach proposed to obtain and deploy these robust plans combines optimization and Monte Carlo simulation. Optimization is used to determine the robust distribution plan and simulation is used to fine-tune the plan's critical parameters such as replenishment cycle times and safety stock levels. Results of a simplified real-life case implementing the proposed optimization-simulation approach are shown and discussed in detail.     

Productivity and technical changes in the Indian pharmaceutical industry

We study the productivity change and factors driving this change in the Indian pharmaceutical industry during 1994–2003, in the backdrop of economic liberalization and change in regulatory norms. We use a non parametric Data Envelopment based-methodology to estimate productivity change and decompose it into technical and relative efficiency changes. We find that, the long-term strategic measures by a section of innovative firms that foresaw the implications from competitive forces of globalization and a change in the regulatory environment have sphereheaded the technical change. Consequently, few innovative firms, characterized by greater R&D investments, transition into higher value-added products and businesses as a step towards more technically sophisticated new drug development have pushed the production frontier, increasing the technical and productivity gains. The higher technical and R&D capabilities and wider new product portfolios of multinational companies also have contributed to the positive technical and productivity changes in the Indian pharmaceutical industry.