Additive portfolio improvement and utility-efficient payoffs

How can individual financial contracts be improved in an additive manner, such that any portfolio comprising improved contracts is at least as attractive as the portfolio of original contracts? We show that any additive procedure that improves contracts for all expected utility maximizers is a conditional expectation operator. Improved contracts are also attractive under robust Savage preferences. Furthermore, we generalize Bondarenko’s definition of ‘statistical arbitrage’ and show that the improved contracts do not admit this kind of arbitrage.     

Long-term and penalty contracts in a two-stage supply chain with stochastic demand

Recent applications of game-theoretic analysis to supply chain efficiency have focused on constructs between a buyer (the retailer or manufacturer) and a seller (the supplier) in successive stages of a supply chain. If demand for the final product is stochastic then the supplier has an incentive to keep its capacity relatively low to avoid creating unneeded capacity. The manufacturer, on the other hand, prefers the supplier’s capacity to be high to ensure that the final demand is satisfied. The manufacturer therefore constructs a contract to induce the supplier to increase its production capacity. Most research examines contracting when final demand is realized after the manufacturer places its order to the supplier. However, if final demand is realized before the manufacturer places its order to the supplier, these types of contracts can be ineffective. This paper examines two contracts under the latter timing scenario: long-term contracts in which the business relationship is repeated, and penalty contracts in which the supplier is penalized for too little capacity. Results indicate long-term contracts increase the profit potential of the supply chain. Furthermore, the penalty contracts can ensure that the supplier chooses a capacity level such that the full profit potential is achieved.     

Pareto-optimal reinsurance arrangements under general model settings

In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. For the purpose of practice, we use numerical examples to show how to determine the mutually acceptable Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer’s aim and the reinsurer’s goal can be met under the mutually acceptable Pareto-optimal reinsurance contracts.     

Vendor managed inventory contracts – coordinating the supply chain while looking from the vendor’s perspective

The paper studies coordination of a supply chain when the inventory is managed by the vendor (VMI). We also provide a general mathematical framework that can be used to analyze contracts under both retailer managed inventory (RMI) and VMI. Using a simple newsvendor scenario with a single vendor and single retailer, we study five popular coordinating supply chain contracts: buyback, quantity flexibility, quantity discount, sales rebate, and revenue sharing contracts. We analyze the ability of these contracts to coordinate the supply chain under VMI when the vendor freely decides the quantity. We find that even though all of them coordinate under RMI, quantity flexibility and sales rebate contracts do not generally coordinate under VMI. Furthermore, buyback and revenue sharing contracts are equivalent. Hence, we propose two new contracts which coordinate under VMI (one of which coordinates under RMI too, provided a well-known assumption holds). Finally, we extend our analysis to consider multiple independent retailers with the vendor incurring linear or convex production cost, and show that our results are qualitatively unchanged.     

The efficiency of financial futures markets: Tests of prediction accuracy

The prices of financial futures contracts can be interpreted as forecasts of the spot rates, which will apply at the final delivery date of that contract. Financial futures contracts have been traded daily since the early 1980s and provide a substantial bank of data to test the forecasting efficiency of such contracts. Tests are carried out to examine whether the interest rates implied by the futures price for eurodollar and short sterling contracts are cointegrated with the final settlement price over forecasting horizons of 1, 2 and 3 months. Similar analysis is carried out for the yen/dollar exchange rate futures contract. The paper then examines the forecasting performance of the three contracts over the forecasting horizons of 1, 2 and 3 months and in particular whether the forecasts implied by the futures contract provide better predictions than the naı̈ve no-change (i.e. random walk), a vector error correction model (VECM) or an ARIMA model.An examination of the relative efficiency of the markets for the three markets over the three time horizons is carried out and finally trading strategies are simulated to see whether excess profits can be achieved. In fact the results suggest that both profits and losses would be attracted.     

Pareto-optimal contracts for a supply chain with satisficing objectives

We analyse a decentralized supply chain consisting of a supplier and a retailer, each with a satisficing objective, that is, to maximize the probability of achieving a predetermined target profit. The supply chain is examined under two types of commonly used contracts: linear tariff contracts (including wholesale price contracts as special cases) and buy-back contracts. First, we identify the Pareto-optimal contract(s) for each contractual form. In particular, it is shown that there is a unique wholesale price that is Pareto optimal for both contractual types. Second, we evaluate the performance of the Pareto-optimal contracts. In contrast to the well-known results for a supply chain with the traditional expected profit objectives, we show that wholesale price contracts can coordinate the supply chain whereas buy-back contracts cannot. This provides an additional justification for the popularity of wholesale price contracts besides their simplicities and lower administration costs.     

看涨期权契约与看跌期权契约对比分析研究

在面临相同随机市场需求的情况下,本文对期权契约中的看涨期权与看跌期权契约进行了对比分析,以期为决策者在实际采购活动中选择不同类型的期权契约时提供决策依据。通过模型建立与求解分析,本文得出了销售商接受期权契约时,契约参数需要满足的条件及相应的订购策略;并进一步得出了两种期权契约下,供应链达到协调状态时的具体条件,分析了此时契约参数对供销双方利润的影响,继而给出了两种期权契约的适用范围以及供销双方的契约选择偏好。在此基础上,本文还给出了不同期权契约下,供销双方各自利润均不低于其自身保留利润时契约参数的取值范围,并证明了两种期权契约均可有效提高销售商的利润水平。最后,本文通过算例对上述结论进行了验证。     

Optimal contracts in portfolio delegation

The optimal contracts in portfolio delegation under general preferences are characterized when the underlying state variable is not contractible, and the principal must rely on the final returns of portfolios to design the compensation schemes for the fund manager. We show that the optimal contracts satisfy a second-order nonlinear ordinary differential equation that depends on the utility functions and the distribution of state price density. In general, there is an efficiency loss for the optimal contracts unless the utility functions of both the principal and the agent exhibit linear risk tolerance with identical cautiousness. Additional contractible observables, like stock indexes, can be used to improve the efficiency of the second-best contracts, even if they are not perfectly correlated with the underlying state price. A continuous-time example with power utilities is presented to illustrate the features of the optimal contracts.     

Optimal procurement strategies for online spot markets

Spot markets have emerged for a broad range of commodities, and companies have started to use them in addition to their traditional, long-term procurement contracts (forward contracts). In comparison to forward contracts, spot markets offer products at essentially negligible lead time, but typically command a higher expected price for this added flexibility while also exhibiting substantial price uncertainty. In our research, we analyze the resulting procurement challenge and quantify the benefits of using spot markets from a supply chain perspective. We develop and solve mathematical models that determine the optimal order quantity to purchase via forward contracts and the optimal quantity to purchase via spot markets. We analyze the most general situation where commodities can be both bought and sold via a spot market and derive closed-form results for this case. We compare the obtained results to the reference scenario of pure contract sourcing and we include results for situations where the use of spot markets is restricted to either buying or selling only. Our approaches can be used by decision makers to determine optimal procurement strategies based on key parameters such as, demand and spot price volatilities, correlation between demand and spot prices, and risk aversion. The results of our analysis demonstrate that significant profit improvements can be achieved if a moderate fraction of the commodity demand is procured via spot markets. The results also show that companies who use spot markets can offer a higher expected service level, but that they might experience a higher variability in profits than companies who do not use spot markets. We illustrate our analytical results with numerical examples throughout the paper.     

Pricing and clearing combinatorial markets with singleton and swap orders

In this article we consider combinatorial markets with valuations only for singletons and pairs of buy/sell-orders for swapping two items in equal quantity. We provide an algorithm that permits polynomial time market-clearing and -pricing. The results are presented in the context of our main application: the futures opening auction problem. Futures contracts are an important tool to mitigate market risk and counterparty credit risk. In futures markets these contracts can be traded with varying expiration dates and underlyings. A common hedging strategy is to roll positions forward into the next expiration date, however this strategy comes with significant operational risk. To address this risk, exchanges started to offer so-called futures contract combinations, which allow the traders for swapping two futures contracts with different expiration dates or for swapping two futures contracts with different underlyings. In theory, the price is in both cases the difference of the two involved futures contracts. However, in particular in the opening auctions price inefficiencies often occur due to suboptimal clearing, leading to potential arbitrage opportunities. We present a minimum cost flow formulation of the futures opening auction problem that guarantees consistent prices. The core ideas are to model orders as arcs in a network, to enforce the equilibrium conditions with the help of two hierarchical objectives, and to combine these objectives into a single weighted objective while preserving the price information of dual optimal solutions. The resulting optimization problem can be solved in polynomial time and computational tests establish an empirical performance suitable for production environments.     

Pareto analysis of supply chain contracts under satisficing objectives

Supply chain coordination has become critical to firms as increased pressure is placed on them to improve performance. We evaluate the performance of Push, Pull, and Advance-purchase discount (APD) contracts in a manufacturer-retailer supply chain where one or both firms have a satisficing objective of maximizing the probability of achieving a target profit. We identify the resulting operational modes of the supply chain and potential conflicts over the preferred contracts under the Push, Pull, and APD contracts. When both firms are satisficing, conflict over the preferred contract arises when the manufacturer has an ambitious profit target or the retailer has a low profit target. We show that the Push contract can result in a large decrease in the expected profit of a risk-neutral manufacturer when the retailer maximizes the probability of achieving her maximum expected profit. We find that a modified buy-back and profit guarantee contracts can provide significant Pareto improvement over Push or APD contracts when the manufacturer is risk-neutral and the retailer is satisficing, while revenue-sharing contracts cannot. In contrast, revenue sharing and modified buy-back contracts are Pareto dominant under certain conditions when the manufacturer is satisficing and the retailer is risk-neutral.     

Revenue-sharing versus wholesale price mechanisms under different channel power structures

We consider a supply chain channel with two manufacturers and one retailer. Each manufacturer can choose either a wholesale price contract or a revenue-sharing contract with the retailer. We discuss and compare the results of two different types of contracts under different channel power structures, to check whether it is beneficial for manufacturers to use revenue-sharing contracts under different scenarios. Then we consider a supply chain channel with one manufacturer and two retailers. Each retailer can choose either a wholesale price contract or a revenue-sharing contract with the manufacturer. We analyze the likely outcomes under different scenarios to discover whether it is beneficial to use revenue-sharing contracts.     

Distribution of Bids for Buildings and Roads Contracts

This paper describes the analysis of data relating to bids for 535 contracts to determine the distribution of these bids. The findings are that bids for building contracts can be treated as samples from a normal distribution and that for roads, although the assumption is statistically less valid, it is adequate for practical purposes. The tests for normality used were the studentized range and the Anderson-Darling statistic. Comments on the uses of these distributions in testing for unrealistic bids and for predicting the lowest bid are given.     

Optimal corrective maintenance contract planning for aging multi‐state system

This paper considers an aging multi‐state system, where the system failure rate varies with time. After any failure, maintenance is performed by an external repair team. Repair rate and cost of each repair are determined by a corresponding corrective maintenance contract with a repair team. The service market can provide different kinds of maintenance contracts to the system owner, which also can be changed after each specified time period. The owner of the system would like to determine a series of repair contracts during the system life cycle in order to minimize the total expected cost while satisfying the system availability. Operating cost, repair cost and penalty cost for system failures should be taken into account. The paper proposes a method for determining such optimal series of maintenance contracts. The method is based on the piecewise constant approximation for an increasing failure rate function in order to assess lower and upper bounds of the total expected cost and system availability by using Markov models. The genetic algorithm is used as the optimization technique. Numerical example is presented to illustrate the approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Flexible contracting theory and case examples

When companies or governmental agencies arrange for contracts that call for deliveries over extended periods of time, arrangements are often made to adjust the final prices for exogenous changes in the costs of production. This paper shows, under specified conditions, how contracts can be devised which allow for price changes but at the same time still provide incentives for the producing unit to be efficient. For example, only under very specific conditions will a “pass-through” arrangement be acceptable. We show how the techniques of Geometric Programming applied to the economic theory of production can be used to analyze such problems.     

Solving nonlinear principal-agent problems using bilevel programming

While significant progress has been made, analytic research on principal-agent problems that seek closed-form solutions faces limitations due to tractability issues that arise because of the mathematical complexity of the problem. The principal must maximize expected utility subject to the agent’s participation and incentive compatibility constraints. Linearity of performance measures is often assumed and the Linear, Exponential, Normal (LEN) model is often used to deal with this complexity. These assumptions may be too restrictive for researchers to explore the variety of relationships between compensation contracts offered by the principal and the effort of the agent. In this paper we show how to numerically solve principal-agent problems with nonlinear contracts. In our procedure, we deal directly with the agent’s incentive compatibility constraint. We illustrate our solution procedure with numerical examples and use optimization methods to make the problem tractable without using the simplifying assumptions of a LEN model. We also show that using linear contracts to approximate nonlinear contracts leads to solutions that are far from the optimal solutions obtained using nonlinear contracts. A principal-agent problem is a special instance of a bilevel nonlinear programming problem. We show how to solve principal-agent problems by solving bilevel programming problems using the ellipsoid algorithm. The approach we present can give researchers new insights into the relationships between nonlinear compensation schemes and employee effort.     

Optimal shared-savings contracts in supply chains: Linear contracts and double moral hazard

In many supply chains consumption of indirect materials, sold by a supplier to a customer for use in her production process, can be reduced by efforts exerted by either party. Since traditional supply contracts provide no incentive for the supplier to exert such effort, shared-savings contracts have been proposed as a way to improve incentives in the channel, leading to more efficient effort choices by the two parties. Such shared-savings contracts typically combine a fixed service fee with a variable component based on consumption volume. We formalize this situation using the double moral hazard framework, in which both parties decide how much effort to exert by trading off the cost of their effort against the benefits that they will obtain from reduced consumption. We also extend the double moral hazard framework to analyze a broader class of cost-of-effort functions than considered so far, including the linear cost-of-effort functions commonly found in practice. We show that the supplier can still always induce the optimal second-best equilibrium with a linear shared-savings contract. Under this broader class of functions, however, the behavior of the optimal contract as a function of the problem parameters becomes more complex. We illustrate how small changes in the problem parameters can turn profits from being a well-behaved to a poorly-behaved function of the contract, and provide some theoretical characterization of this phenomenon. The practical significance of this is that simple (linear) contracts are sufficient in many double moral hazard contexts, even for the broader class of functions we consider, but care must be taken in selecting the optimal contract parameters.     

Channel coordination in a consignment contract

With the emergence of virtual market places, consignment selling has been thriving at an unprecedented pace. It has been shown in the literature that inefficiency exists in a decentralized consignment channel with a single revenue share agreement. In our study, we analyze contracts observed in practice that contain bonus or side payment terms, and examine whether they can promote better coordination between the supplier and the retailer. We found that no multi-tier Bonus system can fully coordinate the consignment channel. However, fine adjustments of bonus parameters can bring the channel close to full coordination. Additionally, we found revenue sharing with side payment contracts not only fully coordinate the channel, but they can also be customized to meet the needs of small, medium and large suppliers for extra retailer services such as warehousing and transportation. Managerial insights on how to design the contracts from the supplier, retailer and channel perspectives are discussed in the paper.     

Transferring and sharing exchange-rate risk in a risk-averse supply chain of a multinational firm

This paper analyzes risk management contracts used to handle currency risk in a decentralized supply chain that consists of risk-averse divisions in a multinational firm. Particular contracts of interest involve transferring risk to a third party by using risk-transfer contracts such as currency options and re-arranging risk between supply chain members using risk-sharing contracts. Due to decentralization, operational and risk management decisions are made locally; however, a headquarter who is interested in total supply chain profit has some controllability over those activities. We question if each kind of risk management contract can improve the utility of all supply chain members compared to the utility without any of those, and how the conditions to achieve such improvements are different. Further structural differences are investigated via sensitivity analysis with respect to the transfer price, the variability of exchange rates, and the location of the headquarter. We also find that using the two kinds of contracts jointly does not necessarily result in better outcomes.     

中国股指期货市场流动性非线性特征分析与波动趋势预测

针对中国股指期货市场的流动性问题,利用多重分形去趋势波动法研究股指期货市场流动性非线性特征及其成因,并对比分析不同期限下期货市场流动性多重分形程度的差异;进一步,采用趋势熵维数方法识别期货市场流动性的变化趋势,还利用识别正确率和随机识别正确率验证该方法有效性和准确性。研究发现,中国股指期货市场具有明显的多重分形特征;与合约期限较短的股指期货相比,合约期限较长的股指期货流动性多重分形程度更低;股指期货市场流动性多重分形特征主要是流动性时间序列的相关多重分形和分布多重分形造成的;趋势熵维数方法可有效预测期货市场流动性的变化趋势。