基于谱风险测度与期权契约的季节性商品订购策略分析
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摘要
以一个经销季节性商品的零售商为研究对象,通过引入考虑零售商风险态度的谱风险测度,分析了期权契约机制下具有不同风险偏好零售商的最优订购策略.通过建立期权契约机制下基于零售商谱风险测度的商品订购决策模型,分析得出零售商的最优现货订购量和期权订购量存在并且唯一;并进一步结合均值-CVaR风险谱函数,研究了在此风险测度下不同风险偏好零售商的具体订购策略,揭示了零售商风险态度、期权契约等对其最优订购策略的影响;最后通过数值实例对模型的求解过程和理论结果进行了验证分析.
Traditional ordering decisions for seasonal products often focus on minimizing expected cost or maximizing expected profits,which assume decision makers to be risk neutral.In this paper,we incorporate retailer's different risk attitudes by means of spectrum risk measure into the ordering decision model for seasonal products,and discuss the optimal ordering decisions of the retailer under the option contract mechanism.We show that the optimal ordering quantities of cash commodity and option commodity are existent and unique,and then analyze the specific ordering strategy of the retailer who has different risk preferences through the mean-CVaR risk spectrum function.The effects of the retailer's risk attitude,and the price parameters of option contract on the optimal ordering decisions are also analyzed.Finally,we illustrate our theoretical results by some numerical examples.
Traditional ordering decisions for seasonal products often focus on minimizing expected cost or maximizing expected profits,which assume decision makers to be risk neutral.In this paper,we incorporate retailer's different risk attitudes by means of spectrum risk measure into the ordering decision model for seasonal products,and discuss the optimal ordering decisions of the retailer under the option contract mechanism.We show that the optimal ordering quantities of cash commodity and option commodity are existent and unique,and then analyze the specific ordering strategy of the retailer who has different risk preferences through the mean-CVaR risk spectrum function.The effects of the retailer's risk attitude,and the price parameters of option contract on the optimal ordering decisions are also analyzed.Finally,we illustrate our theoretical results by some numerical examples.
引文
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[2]Farlow D,Schmidt G,Tsay A.Supplier management at sun microsystems[R].Stanford Business School,1996.
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[4]郭琼,杨德礼,迟国泰.基于期权的供应链契约式协调模型[J].系统工程,2005,23(10):1-6.Guo Q,Yang D L,Chi G T.Supply chain coordination with option contract[J].Systems Engineering,2005,23(10):1-6.
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[6]陈旭.考虑期权合同供应链的零售商订货研究[J].管理科学学报,2006,9(3):17-23.Chen X.Retailer's procurement decisions for supply chain with options contracts[J].Journal of Management Sciences in China,2006,9(3):17-23.
[7]胡本勇,彭其渊,王性玉.考虑采购资金约束的供应链期权柔性契约[J].管理科学学报,2009,12(6):62-71.Hu B Y,Peng Q Y,Wang X Y.Supply chain option flexibility contract with consideration of influence of shortage of capital[J].Journal of Management Sciences in China,2009,12(6):62-71.
[8]Xu H.Managing production and procurement through option contracts in supply chains with random yield[J].International Journal of Production Economics,2010,126(2):306-313.
[9]王婧,陈旭.考虑期权合同的生鲜农产品批发商的最优订货[J].系统工程理论与实践,2010,30(12):2137-2144.Wang J,Chen X.Fresh produce wholesaler's optimal procurement decisions with options contracts[J].Systems Engineering-Theory&Practice,2010,30(12):2137-2144.
[10]Barnes-Schuster D,Bassok Y,Anupindi R.Coordination and flexibility in supply contracts with options[J].Manufacturing&Service Operations Management,2002,4(3):171-207.
[11]Gomez_Padilla A,Mishina T.Supply contract with options[J].International Journal of Production Economics,2009,122(1):312-318.
[12]Zhao Y,Wang S,Cheng T,et al.Coordination of supply chains by option contracts:A cooperative game theory approach[J].European Journal of Operational Research,2010,207(2):668-675.
[13]Eeckhoudt L,Gollier C,Schlesinger H.The risk-averse(and prudent)newsboy[J].Management Science,1995,41(5):786-794.
[14]Agrawal V,Seshadri S.Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem[J].Manufacturing&Service Operations Management,2000,2(4):410-423.
[15]Chen Y,Xu M,Zhang G.A risk averse newsvendor model under CVaR decision criterion[R].Working Paper,The Chinese University of Hong Kong,Hong Kong,China,2006.
[16]Chen F,Federgruen A.Mean-variance analysis of basic inventory models[R].Working Paper,Columbia University,New York,USA,2000.
[17]Choi T M,Li D,Yan H.Mean-variance analysis for the newsvendor problem[J].IEEE Transactions on Systems,Man and Cybernetics,Part A:Systems and Humans,2008,38(5):1169-1180.
[18]Wu J,Li J,Wang S,et al.Mean-variance analysis of the newsvendor model with stockout cost[J].Omega,2009,37(3):724-730.
[19]杨建奎,周清,杨磊.报童模型的利润与亏损风险平衡分析[J].系统工程理论与实践,2009,29(3):100-105.Yang J K,Zhou Q,Yang L.Trade-off analysis of revenue and risk of loss of the newsvendor model[J].Systems Engineering—Theory&Practice,2009,29(3):100-105.
[20](O|¨)zler A,Tan B I,Karaesmen F.Multi-product newsvendor problem with value-at-risk considerations[J].International Journal of Production Economics,2009,117(2):244-255.
[21]Acerbi C,Nordio C,Sirtori C.Expected shortfall as a tool for financial risk management[R].Working Paper,Abaxbank,Milano,Italy,2001.
[22]Szego G.Measures of risk[J].European Journal of Operational Research,2005,163(1):5-19.
[23]Artzner P,Delbaen F,Eber J M,et al.Coherent measures of risk[J].Mathematical Finance,1999,9(3):203-228.
[24]Rockafellar R T,Uryasev S.Optimization of conditional value-at-risk[J].Journal of Risk,2000,2(3):21-42.
[25]Rockafellar R T,Uryasev S.Conditional value-at-risk for general loss distributions[J].Journal of Banking&Finance,2002,26(7):1443-1471.
[26]许明辉,于刚,张汉勤.带有缺货惩罚的报童模型中的CVaR研究[J].系统工程理论与实践,2006,26(10):1-8.Xu M H,Yu G,Zhang H Q.CVaR in a newsvendor model with lost sale penalty cost[J].Systems Engineering—Theory&Practice,2006,26(10):1-8.
[27]Hong L J,Yang Y,Zhang L.Sequential convex approximations to joint chance constrained programs:A Monte Carlo approach[R].Working Paper,The Hong Kong University of Science and Technology,Hong Kong,China,2011.
[28]Acerbi C.Spectral measures of risk:A coherent representation of subjective risk aversion[J].Journal of Banking&Finance,2002,26(7):1505-1518.
[29]Acerbi C,Simonetti P.Portfolio optimization with spectral measures of risk[R].Working Paper,Abaxbank,Milano,Italy,2002.
[30]Choi S,Ruszczynski A.A risk-averse newsvendor with law invariant coherent measures of risk[J].Operations Research Letters,2008,36(1):77-82.
[31]Choi S,Ruszczynski A,Zhao Y.A multiproduct risk-averse newsvendor with law-invariant coherent measures of risk[J].Operations Research,2011,59(2):346-364.
[32]Fichtinger J.The single-period inventory model with spectral risk measures[D].Vienna:WU Vienna University of Economics and Business,2010.
1.为保证随机需求出现负数的可能性极小,故选取正态分布的均值比标准差大三倍以上:同时后文的数值分析和相关结论在均匀分布和指数分布等分布形式中均可得到验证,限于篇幅,本文不再赘述.
[2]Farlow D,Schmidt G,Tsay A.Supplier management at sun microsystems[R].Stanford Business School,1996.
[3]Tsay A A,Lovejoy W S.Quantity flexibility contracts and supply chain performance[J].Manufacturing&Service Operations Management,1999,1(2):89-111.
[4]郭琼,杨德礼,迟国泰.基于期权的供应链契约式协调模型[J].系统工程,2005,23(10):1-6.Guo Q,Yang D L,Chi G T.Supply chain coordination with option contract[J].Systems Engineering,2005,23(10):1-6.
[5]Ritchken P H,Tapiero C S.Contingent claims contracting for purchasing decisions in inventory management[J].Operations Research,1986,34(6):864-870.
[6]陈旭.考虑期权合同供应链的零售商订货研究[J].管理科学学报,2006,9(3):17-23.Chen X.Retailer's procurement decisions for supply chain with options contracts[J].Journal of Management Sciences in China,2006,9(3):17-23.
[7]胡本勇,彭其渊,王性玉.考虑采购资金约束的供应链期权柔性契约[J].管理科学学报,2009,12(6):62-71.Hu B Y,Peng Q Y,Wang X Y.Supply chain option flexibility contract with consideration of influence of shortage of capital[J].Journal of Management Sciences in China,2009,12(6):62-71.
[8]Xu H.Managing production and procurement through option contracts in supply chains with random yield[J].International Journal of Production Economics,2010,126(2):306-313.
[9]王婧,陈旭.考虑期权合同的生鲜农产品批发商的最优订货[J].系统工程理论与实践,2010,30(12):2137-2144.Wang J,Chen X.Fresh produce wholesaler's optimal procurement decisions with options contracts[J].Systems Engineering-Theory&Practice,2010,30(12):2137-2144.
[10]Barnes-Schuster D,Bassok Y,Anupindi R.Coordination and flexibility in supply contracts with options[J].Manufacturing&Service Operations Management,2002,4(3):171-207.
[11]Gomez_Padilla A,Mishina T.Supply contract with options[J].International Journal of Production Economics,2009,122(1):312-318.
[12]Zhao Y,Wang S,Cheng T,et al.Coordination of supply chains by option contracts:A cooperative game theory approach[J].European Journal of Operational Research,2010,207(2):668-675.
[13]Eeckhoudt L,Gollier C,Schlesinger H.The risk-averse(and prudent)newsboy[J].Management Science,1995,41(5):786-794.
[14]Agrawal V,Seshadri S.Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem[J].Manufacturing&Service Operations Management,2000,2(4):410-423.
[15]Chen Y,Xu M,Zhang G.A risk averse newsvendor model under CVaR decision criterion[R].Working Paper,The Chinese University of Hong Kong,Hong Kong,China,2006.
[16]Chen F,Federgruen A.Mean-variance analysis of basic inventory models[R].Working Paper,Columbia University,New York,USA,2000.
[17]Choi T M,Li D,Yan H.Mean-variance analysis for the newsvendor problem[J].IEEE Transactions on Systems,Man and Cybernetics,Part A:Systems and Humans,2008,38(5):1169-1180.
[18]Wu J,Li J,Wang S,et al.Mean-variance analysis of the newsvendor model with stockout cost[J].Omega,2009,37(3):724-730.
[19]杨建奎,周清,杨磊.报童模型的利润与亏损风险平衡分析[J].系统工程理论与实践,2009,29(3):100-105.Yang J K,Zhou Q,Yang L.Trade-off analysis of revenue and risk of loss of the newsvendor model[J].Systems Engineering—Theory&Practice,2009,29(3):100-105.
[20](O|¨)zler A,Tan B I,Karaesmen F.Multi-product newsvendor problem with value-at-risk considerations[J].International Journal of Production Economics,2009,117(2):244-255.
[21]Acerbi C,Nordio C,Sirtori C.Expected shortfall as a tool for financial risk management[R].Working Paper,Abaxbank,Milano,Italy,2001.
[22]Szego G.Measures of risk[J].European Journal of Operational Research,2005,163(1):5-19.
[23]Artzner P,Delbaen F,Eber J M,et al.Coherent measures of risk[J].Mathematical Finance,1999,9(3):203-228.
[24]Rockafellar R T,Uryasev S.Optimization of conditional value-at-risk[J].Journal of Risk,2000,2(3):21-42.
[25]Rockafellar R T,Uryasev S.Conditional value-at-risk for general loss distributions[J].Journal of Banking&Finance,2002,26(7):1443-1471.
[26]许明辉,于刚,张汉勤.带有缺货惩罚的报童模型中的CVaR研究[J].系统工程理论与实践,2006,26(10):1-8.Xu M H,Yu G,Zhang H Q.CVaR in a newsvendor model with lost sale penalty cost[J].Systems Engineering—Theory&Practice,2006,26(10):1-8.
[27]Hong L J,Yang Y,Zhang L.Sequential convex approximations to joint chance constrained programs:A Monte Carlo approach[R].Working Paper,The Hong Kong University of Science and Technology,Hong Kong,China,2011.
[28]Acerbi C.Spectral measures of risk:A coherent representation of subjective risk aversion[J].Journal of Banking&Finance,2002,26(7):1505-1518.
[29]Acerbi C,Simonetti P.Portfolio optimization with spectral measures of risk[R].Working Paper,Abaxbank,Milano,Italy,2002.
[30]Choi S,Ruszczynski A.A risk-averse newsvendor with law invariant coherent measures of risk[J].Operations Research Letters,2008,36(1):77-82.
[31]Choi S,Ruszczynski A,Zhao Y.A multiproduct risk-averse newsvendor with law-invariant coherent measures of risk[J].Operations Research,2011,59(2):346-364.
[32]Fichtinger J.The single-period inventory model with spectral risk measures[D].Vienna:WU Vienna University of Economics and Business,2010.
1.为保证随机需求出现负数的可能性极小,故选取正态分布的均值比标准差大三倍以上:同时后文的数值分析和相关结论在均匀分布和指数分布等分布形式中均可得到验证,限于篇幅,本文不再赘述.