Impacts of risk attitude and outside option on compensation contracts under different information structures

We consider an agency problem where a firm (she) hires a manager (he) who has related managerial expertise to implement a new project. The manager’s managerial expertise is his private information and characterized as an uncertain variable. The revenue brought about by the project in the future is also assumed to be uncertain. In light of these challenges, this paper investigates the impacts of the manager’s risk attitude and the type-and-effort dependent outside option on the optimal compensation contracts under different information structures. Through developing the manager’s decision criterion based on his risk attitude instead of the expected-utility-maximization criterion, we find that, if the manager is conservative and the outside option’s revenue uncertainty is sufficiently high, the optimal commission rate will be distorted upwards under asymmetric managerial expertise information compared with that under symmetric managerial expertise information. Our analysis also confirms that the existence of a type-and-effort dependent outside option distorts up the compensation structure tailored at a fixed outside option. We further show that, comparing with the setting of a fixed outside option when the manager is aggressive, the presence of a type-and-effort dependent outside option results in a surprising phenomenon that the manager’s private information makes no distortion of the firm’s profit.     

A principal–agent problem with heterogeneous demand distributions for a carbon capture and storage system

Mechanism design problems optimize contract offerings from a principal to different types of agents who have private information about their demands for a product or a service. We study the implications of uncertainty in agents’ demands on the principal’s contracts. Specifically, we consider the setting where agents’ demands follow heterogeneous distributions and the principal offers a menu of contracts stipulating quantities and transfer payments for each demand distribution. We present analytical solutions for the special case when there are two distributions each taking two discrete values, as well as a method for deriving analytical solutions from numerical solutions. We describe one application of the model in carbon capture and storage systems to demonstrate various types of optimal solutions and to obtain managerial insights.     

产出不确定条件下“公司+农户”型订单农业供应链协商模型研究

在农产品产出不确定性及零售价格受农产品产出率影响的条件下,研究了一类由风险规避农户和风险中性公司组成“公司+农户”型订单农业农产品供应链协调问题。在该农产品供应链中,农户和公司通过Nash协商谈判来分别决策最优的生产量和订单价格。研究结果表明,在农产品产出不确定及零售市场价格受农产品产出率影响的条件下,风险规避型农户和公司的Nash协商合作博弈存在均衡解。Nash协商谈判所达成的最优农产品产出量和订单价格均高于分散决策情形下的最优农产品产出量和订单价格。最优农产品产出量是关于农户风险规避度的单调增函数,而最优的订单价格是关于农户风险规避度的单调减函数。最后,通过与分散决策情形相比,证明了Nash协商谈判机制能够促使风险规避型农户和风险中性型公司均达到帕累托改进。     

The Optimal Interaction between a Hedge Fund Manager and Investor

ABSTRACT

This study explores hedge funds from the perspective of investors and the motivation behind their investments. We model a typical hedge fund contract between an investor and a manager, which includes the manager’s special reward scheme, i.e., partial ownership, incentives and early closure conditions. We present a continuous stochastic control problem for the manager’s wealth on a hedge fund comprising one risky asset and one riskless bond as a basis to calculate the investors’ wealth. Then we derive partial differential equations (PDEs) for each agent and numerically obtain the unique viscosity solution for these problems. Our model shows that the manager’s incentives are very high and therefore investors are not receiving profit compared to a riskless investment. We investigate a new type of hedge fund contract where the investor has the option to deposit additional money to the fund at half maturity time. Results show that investors’ inflow increases proportionally with the expected rate of return of the risky asset, but even in low rates of return, investors inflow money to keep the fund open. Finally, comparing the contracts with and without the option, we spot that investors are sometimes better off without the option to inflow money, thus creating a negative value of the option.     

Optimal contracting with effort and misvaluation

We propose a new continuous-time contracting model, in which the firm value process can only be observed with noise, and there are two sources of moral hazard: the agent’s effort and misvaluation. The principal can induce the agent to alter the perceived fundamental value of the firm through misvaluation, thus changing the market estimate of that value. We consider two cases in detail: the one in which the market correctly anticipates only the effort, and the other in which it correctly anticipates both the effort and the amount of misvaluation. In the first case, we find that it is optimal for the principal to induce the agent to apply a non-zero amount of misvaluation. Using calculus of variation techniques, we find the optimal pay-per-performance sensitivity (PPS) of the contract and optimal effort and misvaluation amount, by means of solving of a second order ordinary differential equation. In the second case, which can be viewed as an extension of the seminal Holmstrom-Milgrom model to the case of noisy observations, we find that the optimal misvaluation value is zero, and we compare the resulting optimal contract to the Holmstrom-Milgrom contract.     

Optimal dividend-financing strategies in a dual risk model with time-inconsistent preferences

In this paper, we consider an optimal dividend-financing problem for a company whose capital reserve is described by the dual of classical risk model. We assume that the manager of the company has time-inconsistent preferences, which are described by a quasi-hyperbolic discount function, and that financing is permitted to prevent the company from going bankrupt. The manager’s objective is to maximize the expected cumulative dividend payments minus financing costs. We solve the optimization problems for a naive manager and a sophisticated manager, and obtain explicit solutions for both managers. Our results show that the manager with time-inconsistent preferences tends to pay out dividends earlier. We also present some economic implications and sensitivity analysis for our results.     

Selling multiple units to strategic consumers

We consider a monopolist firm selling to strategic customers who may purchase more than one unit of a product in a two-period model. We provide closed-form solutions for the firm’s optimal prices and show that they are non-monotonic in both the value of the second unit and the strategic level of customers. Particularly, the first-period price can increase as customers become more strategic, in contrast to the single-unit setting where it always decreases in the strategic level of customers.     

声誉效应与经理报酬契约的关系研究

探讨了声誉对经理报酬契约的影响 .首先 ,分析了经理效用函数的组成 ,将声誉这个隐性激励约束因素引入经理的效用函数 .随后 ,建立了信息不对称下经理的报酬激励模型 .分析了声誉系数对契约中各要素的影响 ,说明了所有者可以利用经理的声誉效应来设计更加有利的报酬契约 .文章最后给出了主要结论 .     

私募基金规模、申购赎回机制与动态道德风险

运用动态合约理论与实物期权理论研究了私募基金最优激励相容合约的一般特征,考察了基金规模与申购赎回机制对缓解道德风险的作用。结论表明,私募基金最优激励相容合约由投资人的最大预期收益与管理者的最大预期回报共同决定,且购买私募基金类似于做多一种特殊期权,该期权标的资产价格由管理者后续值度量;投资人为激励管理者努力工作而付出的激励成本随基金初始规模或再申购比例递增,而最优基金规模由其边际激励成本与预期边际业绩决定;赎回成本影响投资人的最大预期收益,但对缓解道德风险不具显著作用;适当的业绩抽成可降低道德风险,且业绩抽成与私募基金初始规模或再申购比例在缓解道德风险方面存在一定的替代性。     

Dominance,bargaining power and service platform performance

In this paper we study the relationship between a firm (hotel) and a service platform (Ctrip.com). We start with a newsvendor hotel facing two kinds of customers. D-customers order the room directly from the hotel front desk; C-customers order the room through Ctrip.com. Ctrip.com charges the hotel while introducing its members to the hotel. The hotel decides how many rooms are allotted to Ctrip.com to achieve optimal profit. We consider the situation where one party’s demand cannot be observed by another, and study the commonly used wholesale price contract. Interestingly, the contract can always coordinate the system. We then investigate the influence of bargaining power on the profit division under situations where Ctrip.com and hotel, respectively, dominate the system, and find that increasing (or decreasing) a party’s bargaining power without considering the other does not necessarily benefit (or damage) the first party. Further, we discuss how the parties choose dominance and appropriate bargaining power to make a trade-off for better cooperation. An interesting phenomenon is that bargaining power for each party can be identical when any party dominates the system. We also propose a threshold at which the wholesale price contracts can always be the Pareto optimal for the channel.     

Robust optimal risk sharing and risk premia in expanding pools

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectively or subjectively given probabilistic model. Next, we develop a robust approach by explicitly taking uncertainty about the probabilistic model (ambiguity) into account. The resulting robust certainty equivalents and risk premia compound risk and ambiguity aversion. We provide explicit results on their limits and rates of convergence, induced by Pareto optimal risk sharing in expanding pools.     

A comparison between the robust risk-aware and risk-seeking managers in R&D portfolio management

In this paper, we analyze two mathematical modeling frameworks that reflect different managerial attitudes toward upside risk in the context of R&D portfolio selection. The manager seeks to allocate a development budget between low-risk, low-reward projects, called incremental projects, and high-risk, high-reward projects, called innovational projects. Because of their highly uncertain nature and significant probability of failure, the expected value of the innovational projects is smaller than that of their incremental projects’ counterpart, but the long-term financial health of a company necessitates to take risk in order to maintain growth. We study the differences in strategy and portfolio’s risk profile that arise between a risk-aware manager, who takes upside risk because he has to for the long-term competitive advantage of his company, and a risk-seeking manager, who will take as big a bet as allowed by the model. To the best of our knowledge, this is the first paper to consider upside risk management using a robust-optimization-like methodology.     

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.     

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For a financial or insurance entity, the problem of finding the optimal dividend distribution strategy and optimal firm value function is a widely discussed topic. In the present paper, it is assumed that the firm faces two types of liquidity risks: a Brownian risk and a Poisson risk. The firm can control the time and amount of dividends paid out to shareholders. By sufficiently taking into account the safety of the company, bankruptcy is said to take place at time $t$ if the cash reserve of the firm runs below the linear barrier b+kt (not zero), see 1. We deal with the problem of maximizing the expected total discounted dividends paid out until bankruptcy. The optimal dividend return (or, firm value) function is identified as the classical solution of the associated Hamilton-Jacobi-Bellman (HJB) equation where a second-order differential-integro equation is involved. By solving the corresponding HJB equation, the analytical solution of the optimal firm value function is obtained, the optimal dividend strategy is also characterized, which is of linear barrier type: at time t the firm keeps cash inside when the cash reserves level is less than a critical linear barrier and pays cash in excess of this linear barrier as dividends.     

A stochastic programming model for scheduling call centers with global Service Level Agreements

We consider the issue of call center scheduling in an environment where arrivals rates are highly variable, aggregate volumes are uncertain, and the call center is subject to a global service level constraint. This paper is motivated by work with a provider of outsourced technical support services where call volumes exhibit significant variability and uncertainty. The outsourcing contract specifies a Service Level Agreement that must be satisfied over an extended period of a week or month. We formulate the problem as a mixed-integer stochastic program. Our model has two distinctive features. Firstly, we combine the server sizing and staff scheduling steps into a single optimization program. Secondly, we explicitly recognize the uncertainty in period-by-period arrival rates. We show that the stochastic formulation, in general, calculates a higher cost optimal schedule than a model which ignores variability, but that the expected cost of this schedule is lower. We conduct extensive experimentation to compare the solutions of the stochastic program with the deterministic programs, based on mean valued arrivals. We find that, in general, the stochastic model provides a significant reduction in the expected cost of operation. The stochastic model also allows the manager to make informed risk management decisions by evaluating the probability that the Service Level Agreement will be achieved.     

考虑需求和质量双重风险的动力电池回收定价策略和协调机制研究

合理的定价策略和有效的协调机制是保障即将大量报废的动力电池实现回收利用的重要手段。本文同时考虑动力电池回收利用中来自市场的需求风险和来自回收渠道的质量风险,构建了两阶段逆向供应链分散式和集中式定价模型,发现分散决策下的最优回收价格始终低于集中决策下的最优回收价格,逆向供应链存在双重边际化现象;进一步,基于风险共享契约提出完全补偿契约来协调供应链,从而使供应链成员实现帕累托改进,并结合具体算例提出了相应的建议。     

Pricing surplus server capacity for mean waiting time sensitive customers

We consider a queueing model wherein the resource is shared by two different classes of customers, primary (existing) and secondary (new), under a service level based pricing contract. This contract between secondary class customers and resource manager specifies unit admission price and quality of service (QoS) offered. We assume that the secondary customers’ Poisson arrival rate depends linearly on unit price and service level offered while the server uses a delay dependent priority queue management scheme. We analyze the joint problem of optimal pricing and operation of the resource with the inclusion of secondary class customers, while continuing to offer a pre-specified QoS to primary class customers. Our analysis leads to an algorithm that finds, in closed form expressions, the optimal points of the resulting non-convex constrained optimization problem. We also study in detail the structure and the non-linear nature of these optimal pricing and operating decisions.     

Effects of insurance premium and deductible on production

We consider a risk-averse firm bearing the revenue risk and fuzzy production cost. Using the quadratic utility function the sufficient conditions for a deductible insurance to increase the output are derived and found to be the functions of insurance premium and deductible. We also show that the optimal production for a firm in the fuzzy environment is less than that in the crisp environment.     

Inducing efficiency in oligopolistic markets with increasing returns to scale

We consider a Cournot oligopoly market of firms possessing increasing returns to scale technologies (which may not be identical). It is shown that an external regulating agency can increase total social welfare without running a deficit by offering to subsidize one firm an amount which depends on the output level of that firm and the market price. The firms bid for this contract, the regulator collects the highest bid upfront and subsidizes the highest bidding firm. It is shown that there exists a subsidy schedule such that (i) the regulator breaks even, (ii) the subsidized firm obtains zero net profit and charges a price equal to its average cost, (iii) every other firm willingly exit the market and (iv) market price decreases, consumers are better off and total welfare improves.     

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units

We consider a two-stage supply chain with one supplier and one manufacturer. The manufacturer faces a Poisson demand process where the arrival rate depends on the selling price, the announced delivery time, and the delivery reliability defined as the probability of satisfying the announced delivery time. Such a demand model generalizes the works in the literature by simultaneously considering the above three demand sensitivity factors. The main purpose of this paper is to study the equilibrium decisions in the supply chain with an all-unit quantity discount contract. We consider four scenarios regarding whether the leadtime standard, the delivery reliability standard, and the manufacturer’s capacity are endogenous, and whether the manufacturer’s production cost is its private information. We find that an all-unit quantity discount scheme can coordinate the supply chain for most cases. Managerial insights are observed regarding the impact of the three demand sensitivity factors. For example, the breakpoint in an optimal quantity discount contract always increases with the delivery reliability sensitivity under an exogenous delivery reliability, but may decrease under an endogenous delivery reliability; with asymmetric information, a higher variance of the manufacturer’s unit production costs leads to a lower unit wholesale price for the low-cost manufacturer.