Risk-Averse Co-Decision for Lower-Carbon Product Family Configuration and Resilient Supplier Selection

Due to global pandemics, political unrest and natural disasters, the stability of the supply chain is facing the challenge of more uncertain events. Although many scholars have conducted research on improving the resilience of the supply chain, the research on integrating product family configuration and supplier selection (PCSS) under disruption risks is limited. In this paper, the centralized supply chain network, which contains only one major manufacturer and several suppliers, is considered, and one resilience strategy (i.e., the fortified supplier) is used to enhance the resilience level of the selected supply base. Then, an improved stochastic bi-objective mixed integer programming model is proposed to support co-decision for PCSS under disruption risks. Furthermore, considering the above risk-neutral model as a benchmark, a risk-averse mixed integer program with Conditional Value-at-Risk (CVaR) is formulated to achieve maximum potential worst-case profit and minimum expected total greenhouse gases (GHG) emissions. Then, NSGA-II is applied to solve the proposed stochastic bi-objective mixed integer programming model. Taking the electronic dictionary as a case study, the risk-neutral solutions and risk-averse solutions that optimize, respectively, average and worst-case objectives of co-decision are also compared under two different ranges of disruption probability. The sensitivity analysis on the confidence level indicates that fortifying suppliers and controlling market share in co-decision for PCSS can effectively reduce the risk of low-profit/high-cost while minimizing the expected GHG emissions. Meanwhile, the effects of low-probability risk are more likely to be ignored in the risk-neutral solution, and it is necessary to adopt a risk-averse solution to reduce potential worst-case losses.

Single-stage gradient-based stellarator coil design: stochastic optimization

We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into account coil manufacturing errors. By modeling coil errors independently from the coil discretization, we have the flexibility to consider realistic forms of coil errors. The corresponding stochastic optimization problems are formulated using a risk-neutral approach and risk-averse approaches. We present an efficient, gradient-based descent algorithm which relies on analytical derivatives to solve these problems. In a comprehensive numerical study, we compare the coil designs resulting from deterministic and risk-neutral stochastic optimization and find that the risk-neutral formulation results in more robust configurations and reduces the number of local minima of the optimization problem. We also compare deterministic and risk-neutral approaches in terms of quasi-symmetry on and away from the magnetic axis, and in terms of the confinement of particles released close to the axis. Finally, we show that for the optimization problems we consider, a risk-averse objective using the Conditional Value-at-Risk leads to results which are similar to the risk-neutral objective.

Supply Chain Performance with Target-Oriented Firms

Problem definition: We study a supply chain in which a supplier sets the wholesale price and a retailer responds with an order quantity. Both of the two firms can be either risk-neutral—maximizing the expected profit—or target-oriented, which is to maximize her or his ability to reach a target profit. Academic/practical relevance: Our work not only sheds light on the benefit/loss of trading with target-oriented decision makers but also, adds new knowledge to the supply chain coordination literature. Methodology: We provide strong support for firms’ target-based preference and the linear target formation model through a survey as well as analyzing company data. With the firms’ target-oriented behavior evaluated by a CVaR-satisficing measure, we apply a game theoretical framework to investigate how the target-based preference affects supply chain performance. Results: A firm, be it a supplier or a retailer, is always hurt by its target-based preference but can benefit from its trading partner’s target-based preference. A risk-neutral supplier, for example, can sometimes reap the whole supply chain’s profit if the retailer is target-oriented, and a target-oriented supplier always performs better with a target-oriented retailer than a risk-neutral one. Furthermore, a target-oriented retailer and/or supplier can help alleviate the double-marginalization effect and with a specific target, can help the supply chain achieve the same efficiency level as in a risk-neutral centralized system, with just a wholesale price contract. Another important finding is that if both firms are target-oriented, then the supply chain can have a higher expected profit under a decentralized system than a centralized one. This contrasts with the case when both firms are risk-neutral. We also investigate the role of outside option and retailer-type misidentification and find that both can alleviate the retailer’s disadvantage of being target-oriented. Managerial implications: (i) The target-based preference can be exploited by the trading partner, and hence, a firm should adopt the target-oriented decision criterion with caution. (ii) A target-oriented retailer can explore strategies such as revealing his outside option or hiding his target-based preference in order to be less manipulated. (iii) Whether a firm (and the supply chain) can benefit from its trading partner’s target-based preference often depends on how ambitious the trading partner (and the firm itself if it is target-oriented) sets the target. (iv) Target-based preference of one or both firms can help the supply chain reach the first-best efficiency. (v) When both firms are target-oriented, decentralization can be preferred to centralization.

Risk-Neutral Pricing Method of Options Based on Uncertainty Theory

In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options.

On Market Completions Approach to Option Pricing

Option pricing is one of the most important problems of contemporary quantitative finance. It can be solved in complete markets with non-arbitrage option price being uniquely determined via averaging with respect to a unique risk-neutral measure. In incomplete markets, an adequate option pricing is achieved by determining an interval of non-arbitrage option prices as a region of negotiation between seller and buyer of the option. End points of this interval characterise the minimum and maximum average of discounted pay-off function over the set of equivalent risk-neutral measures. By estimating these end points, one constructs super hedging strategies providing a risk-management in such contracts. The current paper analyses an interesting approach to this pricing problem, which consists of introducing the necessary amount of auxiliary assets such that the market becomes complete with option price uniquely determined. One can estimate the interval of non-arbitrage prices by taking minimal and maximal price values from various numbers calculated with the help of different completions. It is a dual characterisation of option prices in incomplete markets, and it is described here in detail for the multivariate diffusion market model. Besides that, the paper discusses how this method can be exploited in optimal investment and partial hedging problems.

Green Supply Chain Game Model and Contract Design: Risk Neutrality vs. Risk Aversion

This paper incorporates the players’ risk attitudes into a green supply chain (GSC) consisting of a supplier and a retailer. The supplier conducts production and determines the green level and wholesale price as a game leader, the retailer sells green products to consumers and determines the retail price as a follower. Equilibrium solutions are derived, and the influence of risk aversion on the GSC is examined. Our results show that, for the centralized GSC, risk aversion lowers the green level and the retail price; while for the decentralized GSC, risk aversion lowers the wholesale price and the retail price, but it may induce the supplier to increase the green level given a large risk tolerance of the supplier. Meanwhile, the risk-averse decentralized GSC may obtain more expected profit than the risk-neutral decentralized GSC. Furthermore, this paper designs a revenue-and-cost-sharing joint contract to coordinate the risk-neutral GSC, and such a contract can improve the risk-averse GSC under specific conditions.

Continuous-Time Insider Trading with Risk-Neutral Insider under Imperfect Observation

A model of insider trading in continuous time in which a risk-neutral insider possesses long-lived imperfect information on a risk asset is studied. By conditional expectation theory and filtering theory, we turn it into a model with insider knowing complete information about the asset with a revised risky value and deduce its linear Bayesian equilibrium consisting of optimal insider trading strategy and semistrong pricing rule. It shows that, in the equilibrium, as the degree of insider observing the signal of the risky asset value is more and more accurate, market depth, trading intensity, and residual information are all decreasing and the total expectation profit of the insider is increasing and that the information about the asset value incorporated into the equilibrium price, which has nothing to do with the volatility of noise trades, is increasing as time goes by, but not all information of asset value is incorporated into the price in the final disclosed time due to the incompleteness of insider’s observation, though the market depth is still a time-independent constant. Some simulations are illustrated to show these features. However, it is an open question of how to make maximal profit if the insider is risk-averse.

Supply Chain Contract Choice with Different Behavior Preferences of Retailer

Retailer may exhibit irrationality when facing the risk of demand uncertainty; therefore, we consider four retailer behavioral preferences: risk neutral (RN), waste aversion (WA), stockout aversion (SA), and stockout-waste aversion (SW). The decision-making and contract choice of upstream and downstream enterprises in cases where demand depends on supplier’s effort are studied. The results show that if the retailer has only SA or RN preferences, then the supplier prefers to choose a wholesale price contract, while the retailer does the opposite, if the retailer has only WA, then the supplier prefers to choose a revenue sharing contract, but the retailer’s contract choice depends on the degree of waste aversion, and if the retailer has SW, then the contract choice of upstream and downstream enterprises is related to the degree of waste aversion and stockout aversion.