On managerial risk-taking incentives when compensation may be hedged against

We consider a continuous time principal-agent model where the principal/firm compensates an agent/manager who controls the output’s exposure to risk and its expected return. Both the firm and the manager have exponential utility and can trade in a frictionless market. When the firm observes the manager’s choice of effort and volatility, there is an optimal contract that induces the manager to not hedge. In a two factor specification of the model where an index and a bond are traded, the optimal contract is linear in output and the log return of the index. We also consider a manager who receives exogenous share or option compensation and illustrate how risk taking depends on the relative size of the systematic and firm-specific risk premia of the output and index. Whilst in most cases, options induce greater risk taking than shares, we find that there are also situations under which the hedging manager may take less risk than the non-hedging manager.     

产出为Cobb-Dauglas函数的 Holmstrom-Milgrom委托代理模型

Holmstrom-Milgrom模型是在委托代理理论一般化模型的基础上提出的一个简化模型,引入代理人的能力水平,将产出函数从一维的线性函数扩展到二维的非线性Cobb-Dauglas生产函数,分析求解了新的模型.与原模型相比,新的最优解中代理人的努力程度有所提高,风险成本有所降低,委托人的期望收益有所改善.     

Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model

We consider a problem of finding optimal contracts in continuous time, when the agent’s actions are unobservable by the principal, who pays the agent with a one-time payoff at the end of the contract. We fully solve the case of quadratic cost and separable utility, for general utility functions. The optimal contract is, in general, a nonlinear function of the final outcome only, while in the previously solved cases, for exponential and linear utility functions, the optimal contract is linear in the final output value. In a specific example we compute, the first-best principal’s utility is infinite, while it becomes finite with hidden action, which is increasing in value of the output. In the second part of the paper we formulate a general mathematical theory for the problem. We apply the stochastic maximum principle to give necessary conditions for optimal contracts. Sufficient conditions are hard to establish, but we suggest a way to check sufficiency using non-convex optimization.     

Call,put and bidirectional option contracts in agricultural supply chains with sales effort

This paper develops option contracts in a supplier-retailer agricultural supply chain where the market demand depends on sales effort. First, we examine a benchmark case of integrated supply chain with the loss rate. Second, we introduce three coordinating option contracts led by the supplier to reduce the retailer's risk, where the call option contract can reduce the shortage risk, the put option contract can reduce the inventory risk and the bidirectional option contract can reduce the bilateral risk. We find that both the optimal initial order quantity and the optimal option quantity increase with the sales effort and the option price will balance the influence of the loss rate on supply chain coordination. Furthermore, the bidirectional option price is the highest while its option quantity is the least, and the put option initial order quantity is the highest. Third, we also consider an option contract led by the retailer to reduce the supplier's wholesale risk. Among the above four option contracts, we find that the option quantity led by the retailer is the highest. Finally, the numerical examples present the impact of the parameters on the optimal decisions, and provide practical managerial insights to reduce the different risk in the agricultural supply chain.     

Endogenous formation of networks for local public goods

The paper studies a situation in which agents can make a binding agreement both on the amount of local public goods and on the structure of networks through which they share the benefits of public goods. An agent enjoys the benefit of public goods produced by other agents who are (directly or indirectly) connected to him. There is a cost to maintain a link as well as to produce a public good. Because agents can choose the amount of public goods, the value of a link is endogenously determined. We consider two different models of sequential bargaining games through which a contract on allocations is established. In the first model, we allow agents to propose a pure allocation and show that there is no symmetric stationary perfect equilibrium for sufficiently patient agents. In the second model, agents are allowed to propose a distribution on allocations. As a result, we find a symmetric stationary perfect equilibrium in which probabilistic choices are made on an equivalent class of allocations. Subsequently, we characterize core allocations, which consist of a minimally connected network and an effort profile, in which at most one agent does not produce the maximum amount of public good.     

Principal–agent problem for returns handling in a reverse supply chain with one manufacturer and two competing dealers

Focusing on the principal–agent problem in handling new-products returned by customers in a reverse supply chain with one manufacturer and two competing dealers, we investigate how a manufacturer motivates her dealers to exert their efforts to handle and sell the returned new-products using mathematical modelling. By taking into consideration the dealers’ individual rationalities, we design optimal incentive contracts under both symmetric and asymmetric information and obtain the following insights. In the symmetric information situation, dealers’ effort levels are identical to those maximising the expected overall profit of the supply chain. In the asymmetric information situation, however, the dealers’ effort levels are lower than the supply chain optimum. Further, in the case of intensifying competition between the dealers, their effort levels increase, while each dealer’ revenue share received from the manufacturer decreases and the risk, incentive and total agency costs of the entire supply chain tend to diminish. The revenue share is inversely correlated with return uncertainties. When we introduce another random environmental factor affecting returns into the incentive contract, this revenue share increases with a rise in dealers’ effort levels, while the above-mentioned costs of the entire system decline and this improves the supply chain system coordination. The incorporation of fairness into the principal–agent model promotes a further increase in the dealers’ effort levels, which is proved using the fixed-point theorem. Finally, we provide an example to demonstrate the main results.     

企业聘用职业经理人的最优时机及其委托代理模型

认为尽管职业经理人的能力可能更强,但只有当企业规模大于临界规模时,企业才会选择聘用职业经理人.运用实物期权的方法,分析得到了企业聘用职业经理人的最优规模(时机),并基于此建立了最优分成制委托代理模型.分析结果表明,在企业考虑实物期权价值的情况下,增大了聘用职业经理人的临界规模,降低了最优分成比例,提高了代理人的努力水平.结果进一步显示,随着市场不确定性的增大,企业聘用职业经理人的临界规模增大,代理人的努力水平降低,最有分成比例增大.     

阶梯激励合约下代理人行为与合约激励效果

基于委托代理理论研究了阶梯激励合约下的代理人行为,并从委托人角度探讨了最优合约设计的问题。在一般市场需求分布和代理人效用函数下,代理人的效用可能是其努力水平的双峰函数,且存在一个阈值使得当合约绩效奖励超过该阈值时,代理人的努力水平“跳跃式”增加。通过比较阶梯激励合约与其他两类激励合约发现,当代理人是风险厌恶型且代理人的产出完全依赖于其努力水平,委托人总是更偏好阶梯激励合约。     

代理人在职消费对动态多任务激励契约的影响

将代理人的在职消费行为引入到动态多任务委托代理框架中,构造了代理人在职消费行为下的两阶段多任务模型,分析了代理人在职消费行为对动态多任务激励契约的影响.研究结果表明:一是任务为两阶段时,无论代理人有无在职消费行为,代理人的努力程度随着时间均呈上升趋势,这就表明当委托人在设计契约时,如果委托人期望代理人在第一阶段的努力水平不低于第二阶段的努力水平,就需要适当提高第一阶段的业绩薪酬系数;二是代理人在职消费自利行为并不一定会提高自身的努力程度,需要依据在职消费行为对绩效的影响情形来具体分析;三是在两阶段内,代理人存在在职消费时,委托人可适当降低业绩薪酬系数.     

A dynamic principal-agent problem as a feedback Stackelberg differential game

We consider situations in which a principal tries to induce an agent to spend effort on accumulating a state variable that affects the well-being of both parties. The only incentive mechanism that the principal can use is a state-dependent transfer of her own utility to the agent. Formally, the model is a Stackelberg differential game in which the players use feedback strategies. Whereas in general Stackelberg differential games with feedback strategy spaces the leader’s optimization problem has non-standard features that make it extremely hard to solve, in the present case this problem can be rewritten as a standard optimal control problem. A linear-quadratic example is used to illustrate our approach.     

基于质量的IT外包合同设计及分析

考虑了内制与外包两种模式,并以内制模式为基准对IT外包合同进行研究。在外包模式下,分别研究了采取固定价格合同和基于质量的合同时,如何激励接包方付出的努力水平,使其达到内制模式下的最优努力水平,从而使得发包方在满足接包方保留收益的前提下获得更高的期望收益。同时对于影响接包方努力水平的各因素进行了分析。研究结果表明,在一定条件下,选择基于质量、引入奖惩机制的合同将会达到内制模式下的最优努力水平,并能够最大化发包方收益。此外,接包方的努力程度随着激励系数、奖惩系数的增加而增加,但是激励系数会随着奖惩系数的增大而减小,这意味着发包方需要权衡使用奖惩机制。     

Framing contingencies in contracts

This paper develops a contracting model in which the principal frames the contract when the agent is unaware of some contingencies, yet is aware that she may be unaware. We call the contract vague if the agent is still unaware of some contingencies after understanding the contract. We show that the optimal contract is vague if and only if the principal exploits the agent. Applying the model to an insurance problem, we show the insuree is free from exploitation if she slightly underestimates the unforeseen calamities. In a contracting problem, whenever the contractor is unaware of the force majeure event, she is exploited by the employer.     

信贷人存货质押贷款中最优质物甄别合同研究

存货抵押贷款中,信用风险主要来源于抵押物价格和流动性风险,信贷人确定适当的利率和贷款价值比能够有效缓释信用风险。对于已知抵押物价格风险和流动性风险,以信贷市场结构作为约束条件,求解出使信贷人期望利率收益最大化合同利率和贷款价值比。当抵押物流动性风险增加时,信贷人最优贷款合同应该是名义利率和贷款价值比均下降;对于抵押物价格波动满足正态分布的情况,若抵押物价格风险增大,信贷人最优贷款合同应该是名义利率和贷款价值比均上升。数值算例的结果基本验证了以上结论,并与现实情况相接近。     

需求依赖努力水平的农产品供应链期权契约优化

针对供应商和零售商组成的农产品供应链,研究市场需求受到努力水平影响的农产品供应链协调问题.由于双重边际效应,分散式供应链中的最优生产数量低于集中式供应链的情况,零售商努力水平也相对较低.引入期权契约时,在零售商主导期权契约的供应链中,研究得到零售商的最优初始订货量和最优期权价格,以及供应商的最优生产数量,实现供应链协调.数值分析证实了期权契约有助于提高零售商的努力水平以及整个供应链的利润.     

Target market selection and marketing effort under uncertainty: The selective newsvendor

We consider a firm that markets, procures, and delivers a good with a single selling season in a number of different markets. The price for the good is market-dependent, and each market has an associated demand distribution, with parameters that depend on the amount of marketing effort applied. Given long procurement lead-times, the firm must decide which markets it will serve prior to procuring the good. We develop a profit maximizing model to address the firm’s integrated market selection, marketing effort, and procurement decisions. The model implicitly accounts for inventory pooling across markets, which reduces safety stock costs but increases model complexity. The resulting model is a nonlinear integer optimization problem, for which we develop specialized solution methods. For the case in which budget constraints exist, we provide a novel solution approach that uses a tailored branch-and-bound algorithm. Our approach solves a broad range of 3000 test instances in an average of less than 2 seconds, significantly outperforming a leading commercial global optimization solver.     

Optimal and robust contracts for a risk-constrained principal

The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions for the solution to this problem. The second theme of the paper is to discuss how one would actually manage (not just measure) risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal proposes a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation package that induces the agent to select the principal’s optimal choice.     

带有解聘补偿机制的过度自信高管动态激励契约设计研究

考虑具有双边道德风险的委托代理问题,将解聘补偿和过度自信同时引入公司高管的激励契约,构建带有解聘补偿机制的过度自信高管动态激励模型,研究委托人解聘倾向对过度自信高管激励合同设计的影响。结果表明:委托人解聘倾向与高管的过度自信水平呈U型关系,高管代理人努力水平与高管的过度自信水平呈倒U型关系,适度的自信水平能够降低委托人的解聘倾向以及提高高管的努力水平;在引入解聘机制的情境下,解聘补偿能够有效抑制委托人的道德风险,降低委托人的解聘倾向,增加高管两期的努力水平;随着聘期的增加,高管第二期的努力水平低于第一期,委托人第二期的解聘倾向高于第一期;两个合同期内的补偿机制相互影响,表现在第二期的解聘补偿提高了委托人第一期的解聘倾向,导致高管第一期努力水平的下降,而第一期的解聘补偿提高了高管在第二期继续留任的可能性,从而增加了高管和委托人在第二期的期望收益。研究结论对我国企业高管薪酬改革以及长期激励合同设计具有一定的理论参考价值。     

Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.     

Impact of equity and equality on stability and collusion in a decentralized network

We consider a firm that procures a product from a regular supplier whose production is subject to both supply disruption and random yield risks and a backup supplier whose production capacity requires reservation in advance. Under both deterministic and stochastic demand, we study the impact of the two types of supply risks on the firm’s optimal procurement decisions and the importance of correctly identifying the source of supply risks. We find that if the overall supply risk is unchanged but its main source shifts from random yield to supply disruption, the firm should order more from the regular supplier and reserve less capacity from the backup supplier. Ignoring the existence of supply disruption leads to under-utilization of the regular supplier and over-utilization of the backup supplier. Moreover, we examine the option value of the reserved capacity that is affected by the uncertainty of customer demand. We find that the option value increases/decreases in demand uncertainty if the reservation capacity is exercised after/before demand is realized.     

具有随机风险的公司最优投资策略

本文讨论具有随机风险的公司的最优投资策略问题,公司投资选择是存款、贷款及股票交易、,因市场的不完备性,公司在任一时刻存在概率为正值的破产可能性,本文主要结果是：从贷款利率高于存款利率的实际出发,运用最优随机控制理论,得到使公司生存概率取得最大值的最优投资策略,以及相应的最大生存概率,并并对这些结果给出了严格证明。