次分数跳-扩散过程下再装期权定价
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摘要
在股票价格服从次分数Brown运动和跳过程驱动的随机微分方程这个假设基础上,结合次分数Brown运动以及跳过程相关随机分析知识,构建相应数学模型,结合保险精算思想对其求解,从而得到相应的再装期权定价公式。
Based on the assumption that stock price obeys stochastic differential equation driven by sub-fractional Brown motion and jump process,combining sub-fractional Brownian motion and jumping process related stochastic analysis knowledge,constructing a mathematical model for the sub-fractional jump-diffusion process of financial markets.With the help of the actuarial method,the model is solved to obtain the corresponding reload option pricing formula.
Based on the assumption that stock price obeys stochastic differential equation driven by sub-fractional Brown motion and jump process,combining sub-fractional Brownian motion and jumping process related stochastic analysis knowledge,constructing a mathematical model for the sub-fractional jump-diffusion process of financial markets.With the help of the actuarial method,the model is solved to obtain the corresponding reload option pricing formula.
引文
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[2]BLADT M,RYDBERG H T.An actuarial approach to option pricing under the physical measure and without market assumptions[J].Insurance:Mathematics and Economics,1998,22(1):65-73.
[3]薛红,王媛媛.分数Vasicek利率下创新重置期权定价[J].纺织高校基础科学学报,2015,28(1):62-71.
[4]张学莲,薛红.分数布朗运动环境下重置期权定价模型[J].西安工程大学学报,2009,23(4):141-145.
[5]闫海峰,刘三阳.广义Black-Scholes模型期权定价新方法-保险精算方法[J].应用力学和数学,2003,24(7):730-739.
[6]张元庆,蹇明.汇率连动期权的保险精算定价[J].经济数学,2005,22(4):363-367.
[7]毕学慧,杜雪樵.复合期权的保险精算定价[J].合肥工业大学学报(自然科学版),2008,31(8):1343-1346.
[8]郑红,郭亚军,李勇,等.保险精算方法在期权定价模型中的应用[J].东北大学学报(自然科学版),2008,29(3):429-432.
[9]王献东,杜雪樵.跳-扩散环境下的再装期权定价[J].经济数学,2007,24(3):276-282.
[10]何永红,薛红,王晓东.分数布朗运动环境下再装期权的保险精算定价[J].纺织高校基础科学学报,2012,25(3):384-387.
[11]孙玉东,薛红.分数跳-扩散过程下强路径依赖型期权定价模型[J].西安工程大学学报,2010,24(1):122-127.
[12]冯广波,刘再明,候振挺.服从跳-扩散过程的再装期权股票期权的定价[J].系统工程学报,2003,18(1):91-93.
[13]BOJDECKI T,GOROSTIZA L G,TALARCZYK A.Sub-fractional Brownian motion and its relation to occupation times[J].Statistics and Probability Letters,2004,69(4):405-419.
[14]YAN L,HE K,CHEN C.The generalized Bouleau-Yor identity for a sub-fractional Brownian motion[J].Seience China Mathematics,2013,56(10):2089-2116.
[15]肖炜麟,张卫国,徐维军.次分数布朗运动下带交易费用的备兑权证定价[J].中国管理科学,2014,22(5):1-7.
[16]李萍,薛红,李琛伟.分数布朗运动下具有违约风险未定权益[J].纺织高校基础科学学报(自然科学版),2010,32(2):109-112.
[17]贾莉莉,梁向前,姜丽丽.改进的跳-扩散模型下的再装期权定价[J].山东理工大学学报(自然科学版),2009,23(6):86-89.
[2]BLADT M,RYDBERG H T.An actuarial approach to option pricing under the physical measure and without market assumptions[J].Insurance:Mathematics and Economics,1998,22(1):65-73.
[3]薛红,王媛媛.分数Vasicek利率下创新重置期权定价[J].纺织高校基础科学学报,2015,28(1):62-71.
[4]张学莲,薛红.分数布朗运动环境下重置期权定价模型[J].西安工程大学学报,2009,23(4):141-145.
[5]闫海峰,刘三阳.广义Black-Scholes模型期权定价新方法-保险精算方法[J].应用力学和数学,2003,24(7):730-739.
[6]张元庆,蹇明.汇率连动期权的保险精算定价[J].经济数学,2005,22(4):363-367.
[7]毕学慧,杜雪樵.复合期权的保险精算定价[J].合肥工业大学学报(自然科学版),2008,31(8):1343-1346.
[8]郑红,郭亚军,李勇,等.保险精算方法在期权定价模型中的应用[J].东北大学学报(自然科学版),2008,29(3):429-432.
[9]王献东,杜雪樵.跳-扩散环境下的再装期权定价[J].经济数学,2007,24(3):276-282.
[10]何永红,薛红,王晓东.分数布朗运动环境下再装期权的保险精算定价[J].纺织高校基础科学学报,2012,25(3):384-387.
[11]孙玉东,薛红.分数跳-扩散过程下强路径依赖型期权定价模型[J].西安工程大学学报,2010,24(1):122-127.
[12]冯广波,刘再明,候振挺.服从跳-扩散过程的再装期权股票期权的定价[J].系统工程学报,2003,18(1):91-93.
[13]BOJDECKI T,GOROSTIZA L G,TALARCZYK A.Sub-fractional Brownian motion and its relation to occupation times[J].Statistics and Probability Letters,2004,69(4):405-419.
[14]YAN L,HE K,CHEN C.The generalized Bouleau-Yor identity for a sub-fractional Brownian motion[J].Seience China Mathematics,2013,56(10):2089-2116.
[15]肖炜麟,张卫国,徐维军.次分数布朗运动下带交易费用的备兑权证定价[J].中国管理科学,2014,22(5):1-7.
[16]李萍,薛红,李琛伟.分数布朗运动下具有违约风险未定权益[J].纺织高校基础科学学报(自然科学版),2010,32(2):109-112.
[17]贾莉莉,梁向前,姜丽丽.改进的跳-扩散模型下的再装期权定价[J].山东理工大学学报(自然科学版),2009,23(6):86-89.