我国保险资金最优投资结构研究
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摘要
银行业、证券业和保险业是构成我国金融体系的三大支柱行业,新中国成立60年来,三大行业得到了迅速却不平衡的发展。相对于银行业和证券业来说,我国保险业的发展还处于比较落后的状态。保险业的快速发展对促进金融体系和谐发展有着极其重要的作用。而保险业的发展,不仅取决于保险承保业务的规模与效益,还与保险资金投资绩效密切相关。因此,优化我国保险投资结构,提高我国保险资金的投资效果,是促进我国保险业快速发展进而推动我国金融业发展的关键所在。此外,保险资金投资的合理化,对于充分发挥我国保险机构作为机构投资者的作用,促进我国资本市场的稳定发展,以及提高保险业的整体竞争水平也起着至关重要的作用。
自我国保险业恢复以来,保险资金投资经历了无投资阶段、无序投资阶段和逐步完善阶段。在保险资金无投资阶段,我国保险市场供应处于垄断阶段,保险市场供应的主要是产险产品。产险产品资金的特征及其规模很小,对保险资金的投资压力较小。这一时期保险公司的资金基本上都以银行存款的方式进入了银行。在保险资金无序投资阶段,保险市场供应主体迅速增加,保险资金的规模也不断扩大,激发了保险业对资金投资的需求。同时,我国资本市场的迅速发展,为保险资金投资提供了现实的投资渠道。但由于没有专门的保险监管机构,缺乏详细的法规限制和配套的风险控制体系,加上我国资本市场规制也不完善,该阶段的保险资金投资处于无序状态。在保险资金投资逐步完善阶段,1998年11月中国保险监督管理委员会正式成立,代替中国人民银行对保险业实行独立统一的监管,保险监管更加专业化。在这一阶段,保险投资渠道不断拓宽,保险投资工具迅速增长,保险投资结构也更趋合理。
任何一种投资决策都可以用马克维茨理论及其思想进行指导,保险资金的投资是众多投资活动中的一种,当然也离不开Markowitz投资组合理论和最优化思想。但是,保险资金与一般的投资资金相比,具有其特殊性,即安全性、流动性与收益性。所以,运用马克维茨投资理论指导保险资金最优投资模型构建时,不能机械套用,要在原有理论模型的基础上进行适当修改,使之更符合保险资金投资的具体情况。这样建立的模型和求出的最优解才更具有实际应用价值。
在论文的第四部分,作者首先分析了目前影响我国保险资金投资的主要因素。其中,通过系统分析已有文献对承保收益的处理方法,作者认为承保收益不能简单地加入收益目标函数中,应该对其进行单独研究。在分析保险政策限制因素时,文章将现有法规允许的主要投资渠道都纳入到了优化范围内,并首次加入了不动产投资渠道,力求在最大的投资品种范围内达到我国保险资金投资结构的最优。第四部分的另一个重点内容是选取适合保险资金投资的风险度量指标。作者通过比较各类证券投资风险度量指标的优缺点,最终采用了VaR指标,并且选取历史模拟法和公式法分别计算单个资产与投资组合的在险价值。最后,以投资组合的在险价值最小化代替马克维茨模型中的方差最小化作为目标函数,以影响我国保险投资的限制因素作为约束条件,文章建立了符合我国实际情况的保险资金最优投资模型。
文章的第五部分是实证分析。作者用证券市场上的相关指数来代表模型中各投资品种的表现,通过2005年4月到2009年7月代表指数的历史收盘价格,计算出了各代表指数的月收益率数据,也即保险资金投资资产种类的期望收益率,并由此得出了模型中的其他数据。为了强调投资风险的重要性,文章将保险最优投资模型中的风险目标函数转换为约束条件,并设定了不同的资金损失率水平,然后利用MATLAB优化工具箱求出了模型的最优解,即我国保险资金的最优投资结构。对于该最优投资结构,本文还做了进一步的对比分析,并得出几个重要结论:我国保险资金投资结构仍需进一步改善;增加不动产投资渠道使保险公司所面临的投资组合有效边界向左上方移动了,即在同等的风险水平下,保险投资组合可获得更高的收益;必须严格限制不动产投资比例。这三个结论和本文求出的保险资金最优投资结构都是在实证的基础上得到的,对我国保险资金今后的投资行为有一定的实际参考价值。
Banking,securities and insurance are the three major industries in Chinese financial system.Their growth has been rapid but uneven in the 60 years since the founding of P.R.C.The insurance industry is still behind from the other two.The rapid development of the insurance industry has an extremely important role on promoting the harmony of our financial system.The development of insurance industry depends not only on the size and profit of underwriting,but also closely on the investment performance.Therefore,optimizing the investment structure and improving the investment performance are the keys to promote the development of our country's insurance,even the finance,industry.Additionally,the rationalization of insurance investment is also very important for insurance companies to playing an institutional investor role,for promoting stable capital market and raising the overall competition level of insurance industry in China.
Since the industry was restarted in China,it has experienced three periods of no investment,disordered investment and gradually improved.In the period of no investment,the insurance supply market is monopoly,it mainly supplies property insurance.There is small stress for the insurance investment.The insurance funds were deposited into the bank.In the period of disorder investment,the number of insurance companies was increased rapidly.The size of insurance funds was also expanded.They stimulated investment needs.And the rapid development of Chinese capital market provided a realistic investment channels.However,there was no specific insurance regulator,less detailed regulatory and risk control system.The capital market regulation is not perfect also.So,the insurance funds were invested disorderly.In the third period,China Insurance Regulatory Commission was formally established in November 1998,replacing the People's Bank to regulate insurance industry.The insurance regulation is more professional.And in this period,the investment channels are broaden continuously,the investment vehicles grow rapidly, the structure of insurance investment is also more reasonable.
Any investment decision can be carried out with the Markowitz Theory and its ideological guidance.Insurance investment is one of investment activities,and can be guided by them certainly.But there are some features in insurance funds:safety, liquidity and profitability.So,the Markowitz portfolio theory can't be applied directly. It must be changed appropriately.Thus,the optimal investment model is more in accordance with the facts.And the solution is more practically valuable.
In the fourth section,it is firstly analyzed that the main factors which are impacting the Chinese insurance investment currently.In this process,after the systematic analysis of the ways using the underwriting income in the existing literatures,the author believes that it can't be simply added to the revenue objective function.It is also believed that the underwriting income should be studied separately. In the process of analyzing the policy limiting to insurance investment,all main investment channels allowed by the existing regulations are in the scope of optimizing. It is the first time to involve real estate.The purpose is to find the optimal insurance investment structure within the largest range.Another focus in PartⅣis selecting appropriate indicator measuring the risks of insurance investment.By comparing various risk measurements,VaR is used finally.The historical simulation method and the formula method are selected to calculate the value at risk of individual asset and portfolio.Finally,using the minimum value at risk instead of variance of the portfolio as the objective function in Markowitz model,and using the factors affecting Chinese insurance investment as constraints,the optimal model of insurance investment in accordance with China's actual situation was established.
The fifth part is empirical analysis.The relevant stock market indices were used to represent the assets' performance.The index's return data,which represent the expected return of assets invested,are calculated with their historical monthly closing prices from April 2005 to July 2009.Thus,the other data are obtained.In order to emphasize the importance of investment risk,the risk objective function is converted to one constraint of the optimal insurance investment model,and it is given some different values.Using the optimization toolbox in MATLAB,the optimal solution is derived.That means,the optimal structure of insurance investment in China is obtained.There is a further comparative analysis on the basis of the optimal structure above.And several important conclusions are drawn from the analysis:The investment structure in Chinese insurance need to be further improved;The insurance companies face a higher portfolio efficient frontier after the real estate investment channel is added,that is,the companies can achieve a higher return at the same level of risk;The ratio of real estate invested must be strictly limited.The three conclusions before and the optimal structure of insurance investment are based on the facts in China.So,they have some practical values for future investment behavior of insurance in practice.
自我国保险业恢复以来,保险资金投资经历了无投资阶段、无序投资阶段和逐步完善阶段。在保险资金无投资阶段,我国保险市场供应处于垄断阶段,保险市场供应的主要是产险产品。产险产品资金的特征及其规模很小,对保险资金的投资压力较小。这一时期保险公司的资金基本上都以银行存款的方式进入了银行。在保险资金无序投资阶段,保险市场供应主体迅速增加,保险资金的规模也不断扩大,激发了保险业对资金投资的需求。同时,我国资本市场的迅速发展,为保险资金投资提供了现实的投资渠道。但由于没有专门的保险监管机构,缺乏详细的法规限制和配套的风险控制体系,加上我国资本市场规制也不完善,该阶段的保险资金投资处于无序状态。在保险资金投资逐步完善阶段,1998年11月中国保险监督管理委员会正式成立,代替中国人民银行对保险业实行独立统一的监管,保险监管更加专业化。在这一阶段,保险投资渠道不断拓宽,保险投资工具迅速增长,保险投资结构也更趋合理。
任何一种投资决策都可以用马克维茨理论及其思想进行指导,保险资金的投资是众多投资活动中的一种,当然也离不开Markowitz投资组合理论和最优化思想。但是,保险资金与一般的投资资金相比,具有其特殊性,即安全性、流动性与收益性。所以,运用马克维茨投资理论指导保险资金最优投资模型构建时,不能机械套用,要在原有理论模型的基础上进行适当修改,使之更符合保险资金投资的具体情况。这样建立的模型和求出的最优解才更具有实际应用价值。
在论文的第四部分,作者首先分析了目前影响我国保险资金投资的主要因素。其中,通过系统分析已有文献对承保收益的处理方法,作者认为承保收益不能简单地加入收益目标函数中,应该对其进行单独研究。在分析保险政策限制因素时,文章将现有法规允许的主要投资渠道都纳入到了优化范围内,并首次加入了不动产投资渠道,力求在最大的投资品种范围内达到我国保险资金投资结构的最优。第四部分的另一个重点内容是选取适合保险资金投资的风险度量指标。作者通过比较各类证券投资风险度量指标的优缺点,最终采用了VaR指标,并且选取历史模拟法和公式法分别计算单个资产与投资组合的在险价值。最后,以投资组合的在险价值最小化代替马克维茨模型中的方差最小化作为目标函数,以影响我国保险投资的限制因素作为约束条件,文章建立了符合我国实际情况的保险资金最优投资模型。
文章的第五部分是实证分析。作者用证券市场上的相关指数来代表模型中各投资品种的表现,通过2005年4月到2009年7月代表指数的历史收盘价格,计算出了各代表指数的月收益率数据,也即保险资金投资资产种类的期望收益率,并由此得出了模型中的其他数据。为了强调投资风险的重要性,文章将保险最优投资模型中的风险目标函数转换为约束条件,并设定了不同的资金损失率水平,然后利用MATLAB优化工具箱求出了模型的最优解,即我国保险资金的最优投资结构。对于该最优投资结构,本文还做了进一步的对比分析,并得出几个重要结论:我国保险资金投资结构仍需进一步改善;增加不动产投资渠道使保险公司所面临的投资组合有效边界向左上方移动了,即在同等的风险水平下,保险投资组合可获得更高的收益;必须严格限制不动产投资比例。这三个结论和本文求出的保险资金最优投资结构都是在实证的基础上得到的,对我国保险资金今后的投资行为有一定的实际参考价值。
Banking,securities and insurance are the three major industries in Chinese financial system.Their growth has been rapid but uneven in the 60 years since the founding of P.R.C.The insurance industry is still behind from the other two.The rapid development of the insurance industry has an extremely important role on promoting the harmony of our financial system.The development of insurance industry depends not only on the size and profit of underwriting,but also closely on the investment performance.Therefore,optimizing the investment structure and improving the investment performance are the keys to promote the development of our country's insurance,even the finance,industry.Additionally,the rationalization of insurance investment is also very important for insurance companies to playing an institutional investor role,for promoting stable capital market and raising the overall competition level of insurance industry in China.
Since the industry was restarted in China,it has experienced three periods of no investment,disordered investment and gradually improved.In the period of no investment,the insurance supply market is monopoly,it mainly supplies property insurance.There is small stress for the insurance investment.The insurance funds were deposited into the bank.In the period of disorder investment,the number of insurance companies was increased rapidly.The size of insurance funds was also expanded.They stimulated investment needs.And the rapid development of Chinese capital market provided a realistic investment channels.However,there was no specific insurance regulator,less detailed regulatory and risk control system.The capital market regulation is not perfect also.So,the insurance funds were invested disorderly.In the third period,China Insurance Regulatory Commission was formally established in November 1998,replacing the People's Bank to regulate insurance industry.The insurance regulation is more professional.And in this period,the investment channels are broaden continuously,the investment vehicles grow rapidly, the structure of insurance investment is also more reasonable.
Any investment decision can be carried out with the Markowitz Theory and its ideological guidance.Insurance investment is one of investment activities,and can be guided by them certainly.But there are some features in insurance funds:safety, liquidity and profitability.So,the Markowitz portfolio theory can't be applied directly. It must be changed appropriately.Thus,the optimal investment model is more in accordance with the facts.And the solution is more practically valuable.
In the fourth section,it is firstly analyzed that the main factors which are impacting the Chinese insurance investment currently.In this process,after the systematic analysis of the ways using the underwriting income in the existing literatures,the author believes that it can't be simply added to the revenue objective function.It is also believed that the underwriting income should be studied separately. In the process of analyzing the policy limiting to insurance investment,all main investment channels allowed by the existing regulations are in the scope of optimizing. It is the first time to involve real estate.The purpose is to find the optimal insurance investment structure within the largest range.Another focus in PartⅣis selecting appropriate indicator measuring the risks of insurance investment.By comparing various risk measurements,VaR is used finally.The historical simulation method and the formula method are selected to calculate the value at risk of individual asset and portfolio.Finally,using the minimum value at risk instead of variance of the portfolio as the objective function in Markowitz model,and using the factors affecting Chinese insurance investment as constraints,the optimal model of insurance investment in accordance with China's actual situation was established.
The fifth part is empirical analysis.The relevant stock market indices were used to represent the assets' performance.The index's return data,which represent the expected return of assets invested,are calculated with their historical monthly closing prices from April 2005 to July 2009.Thus,the other data are obtained.In order to emphasize the importance of investment risk,the risk objective function is converted to one constraint of the optimal insurance investment model,and it is given some different values.Using the optimization toolbox in MATLAB,the optimal solution is derived.That means,the optimal structure of insurance investment in China is obtained.There is a further comparative analysis on the basis of the optimal structure above.And several important conclusions are drawn from the analysis:The investment structure in Chinese insurance need to be further improved;The insurance companies face a higher portfolio efficient frontier after the real estate investment channel is added,that is,the companies can achieve a higher return at the same level of risk;The ratio of real estate invested must be strictly limited.The three conclusions before and the optimal structure of insurance investment are based on the facts in China.So,they have some practical values for future investment behavior of insurance in practice.
引文
[1]北京日报,《A股机构投资者超六成》,2009年8月26日。
[2]参见邢天才著,《中外资本市场比较研究》,东北财经大学出版社,2003版,第69页。
[3]殷剑峰著,《中国金融产品与服务报告2007》,社会科学文献出版社出版,2007版,第14页。
[4]数据来源于中国保险监督管理委员会网站http://www.circ.gov.cn/.
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[3]宋锐主编,《保险基础》,电子工业出版社,2007版,第13页。
[4]由国家统计局公布的《2008中国统计年鉴》中相关数据整理得出。
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[1]杜鹃著,《保险学基础第二版》,上海财经大学出版社,2007版,第230页。
[1]由中宏统计数据库相关数据整理得到。
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[27]汪婷婷.VAR模型在测算我国产险公司资产风险资本额中的应用:[硕士毕业论文]。湖南:湖南大学图书馆,2006.
[28]谷秀娟.金融风险管理理论、技术与应用.北京:立信会计出版社,2006.224
[29]李毓.金融风险的度量与管理.吉林:吉林人民出版社,2007.103-107
[30]杜本峰.机构投资者投资风险管理.北京:经济科学出版社,2004.78-105
[31]陈辉,陈建成.我国保险投资组合的模拟和金融风险测量研究.统计研究,2008,(11):65-71
[32]傅莉莉.保险资金运用中的风险度量—VaR模型分析.金融财务,2007,(11):77-79
[33]王肃元.保险法学.北京:中国人民公安大学出版社,2003.181-283
[34]Harry Markowitz.Portfolio Selection:Efficient Diversification of Investment.The Journal of Finance,1952,7(1):77-91
[35]William F Sharpe.Capital Asset Prices:A Theory of Market Equilibrium under Conditions of Risk.The Journal of Finance,1964,19(3):425-442
[36]John Lintner.The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.The Review of Economics and Statistics,1965,47(1):13-37
[37]Jan Mossin.Equilibrium in a Capital Asset Market.Econometrics,1966,34(4):768-783
[38]Stephen A.Ross.The Arbitrage Theory of Capital Asset Pricing.Journal of Economic Theory,1976,13(3):341-360
[39]Li,Duan;Ng,Wan-Lung.Optimal Dynamic Portfolio Selection:Multiperiod Mean-Variance Formulation.Mathematical Finance,2000,10(3):387-406
[40]Li D,Chan T.F and Ng WL.Safety-first dynamic portfolio selection.Dynamics of Continuous,Discrete and Impulsive Systems,1998,(4):585-600
[41]Fama E F. Multi-period continuous-investment decisions. American Economic Review, 1970, (6): 163—174
[42]Nils H. Hakansson. Multi-period mean-variance analysis: Toward a general theory of portfolio choice. The Journal of Finance, 1971, 26(4):857—884
[43] Edwin J. Elton; Martin J. Gruber. On the optimality of some multiperiod portfolio selection criteria. The Journal of Business, 1974, 47 (2):231—243
[44]Merton RC. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 1971,(3):373—413
[45]Merton RC. Continuous-Time Finance. Cambridge: MA & Oxford, UK, 1990. 308-425
[46]Karatzas I, Wang H. Utility maximization with discretion ray stopping. Stamj Control and Optimization, 2000, 39(1):306-329
[47] Eugene W. Lambert, Alfred E. Hofflander, Impact of new multiple line underwriting on investment portfolios of property-liability insurers. The Journal of Risk and Insurance, 1966, 33 (2):209—223
[48]Krouse, Clement G, Portfolio balancing corporate assets and liabilities with special application to insurance management. The Journal of Financial and Quantitative Analysis, 1970, 5(1), 77—104
[49] Yehuda Kahane, David Nye. A portfolio approach to the property-liability insurance industry. Risk and Insurance, 1975,42(4):579—598
[50] Yehuda Kahane. Generation of investable funds and the portfolio behavior of the non-life insurance. The Journal of Risk and Insurance, 1978,45(1) :65—77
[51] Frost, A.J. Implications of modern portfolio theory for lift assurance companies. The Journal of the Institute of Actuaries, 1983, 26(1):47-68
[52]Petterson, J.A. The dependence of investment policy on the liabilities of a lift office. Transactions of the 22nd International Congress of Actuaries in Sydney, 1984, (15): 201-215
[2]参见邢天才著,《中外资本市场比较研究》,东北财经大学出版社,2003版,第69页。
[3]殷剑峰著,《中国金融产品与服务报告2007》,社会科学文献出版社出版,2007版,第14页。
[4]数据来源于中国保险监督管理委员会网站http://www.circ.gov.cn/.
[1]宋锐主编,《保险基础》,电子工业出版社,2007版,第12页。
[2]何德旭主编,《中国服务业发展报告No.7》,社会科学文献出版社,2008版,第53页。
[3]宋锐主编,《保险基础》,电子工业出版社,2007版,第13页。
[4]由国家统计局公布的《2008中国统计年鉴》中相关数据整理得出。
[1]杨老金、邹照洪,《我国债券市场的发展历程》,中国养老金网www.cnpension.net.
[2]杜鹃著,《保险学基础第二版》,上海财经大学出版社,2007版,第228页。
[1]杜鹃著,《保险学基础第二版》,上海财经大学出版社,2007版,第230页。
[1]由中宏统计数据库相关数据整理得到。
[2]刘紫云,陈家洪,李明哲,《浮动利率、汇率制度下保险资金投资管理研究》,价格月刊,2009年第3期。
[1]王明涛著,《证券投资风险计量、预测与控制》,上海财经大学出版社,2003版,第59页。
[1]王肃元著,《保险法学》,中国人民公安大学出版社,2003版,第181-283页。
[1]邢天才.中外资本市场比较研究.大连:东北财经大学出版社,2003.69-69
[2]中国保险监督管理委员会网站http://www.circ.gov.cn/
[3]陆爱勤.保险投资组合策略研究.上海金融,2007,(10):79-82
[4]贺翠芹.保险资金投资战略分析.济南大学学报,2002,(12):70-72
[5]蒋洪浪.保险投资的资金配置策略.保险研究,2002,(8):34-35
[6]郭文旌,雷鸣.跳跃盈余下的保险最优投资.兰州大学学报,2008,(8):118-122
[7]安实,张炀,陈剑平.基于差异系数σ/μ的人寿保险公司最优投资组合方法.管理工程学报,2003,(3):99-101
[8]秦振球,俞自由.保险公司投资比例问题研究.财经研究,2003,(2):41-47
[9]荣喜民,李楠.保险基金的最优投资研究.数量经济技术经济研究,2004,(10):62-67
[10]曹怡.我国保险投资现状及最优投资组合研究:[硕士毕业论文]。天津:天津大学图书馆,2005.
[11]郝佳,范强华.关于我国保险资金最优投资组合的实证研究.海南金融,2007,(8):26-32
[12]方立雄.保险公司最优投资比例的选择.开放导报,2007,(8):108-110
[13]张笑伟.保险资金最优投资组合研究及评价.廊坊师范学院学报,2008,(8):82-84
[14]胡太华.我国保险投资组合优化研究:[硕士毕业论文]。北京:北京交通大学图书馆,2008.
[15]涂洪,朱正佑.保险公司中的最优分红和投资组合及其数值计算.上海大学学报,2008,(2):65-69
[16]郭文旌,胡奇英.不确定终止时间的多阶段最优投资组合.管理科学学报,2005,(4):13-19
[17]林浩.投资组合问题的动态规划方法.运筹与管理,2000,(9):102-106
[18]李伯德.最优投资组合的数学模型与案例分析.兰州商学院学报,2006,(4):97-99
[19]杜鹃.保险学基础.第二版.上海:上海财经大学出版社,2007.228-230
[20]刘紫云,陈家洪,李明哲.浮动利率、汇率制度下保险资金投资管理研究.价格月刊,2009,(3):48-51
[21]滋维.博迪.投资学.第五版.朱宝宪译.北京:机械工业出版社,2004.385-402
[22]张亦春.金融市场学.北京:高等教育出版社,1999.174-176,200
[23]赵静.数学建模与数学实验.第三版.北京:高等教育出版社,2008.83-91
[24]陈学华,韩兆洲,唐珂.基于VaR和RAROC的保险基金最优投资研究.数量经济技术经济研究,2006,(4):111-117
[25]申曙光.现代保险学教程.北京:高等教育出版社,2003.198-200
[26]王明涛.证券投资风险计量、预测与控制.上海:上海财经大学出版社,2003.57-59
[27]汪婷婷.VAR模型在测算我国产险公司资产风险资本额中的应用:[硕士毕业论文]。湖南:湖南大学图书馆,2006.
[28]谷秀娟.金融风险管理理论、技术与应用.北京:立信会计出版社,2006.224
[29]李毓.金融风险的度量与管理.吉林:吉林人民出版社,2007.103-107
[30]杜本峰.机构投资者投资风险管理.北京:经济科学出版社,2004.78-105
[31]陈辉,陈建成.我国保险投资组合的模拟和金融风险测量研究.统计研究,2008,(11):65-71
[32]傅莉莉.保险资金运用中的风险度量—VaR模型分析.金融财务,2007,(11):77-79
[33]王肃元.保险法学.北京:中国人民公安大学出版社,2003.181-283
[34]Harry Markowitz.Portfolio Selection:Efficient Diversification of Investment.The Journal of Finance,1952,7(1):77-91
[35]William F Sharpe.Capital Asset Prices:A Theory of Market Equilibrium under Conditions of Risk.The Journal of Finance,1964,19(3):425-442
[36]John Lintner.The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.The Review of Economics and Statistics,1965,47(1):13-37
[37]Jan Mossin.Equilibrium in a Capital Asset Market.Econometrics,1966,34(4):768-783
[38]Stephen A.Ross.The Arbitrage Theory of Capital Asset Pricing.Journal of Economic Theory,1976,13(3):341-360
[39]Li,Duan;Ng,Wan-Lung.Optimal Dynamic Portfolio Selection:Multiperiod Mean-Variance Formulation.Mathematical Finance,2000,10(3):387-406
[40]Li D,Chan T.F and Ng WL.Safety-first dynamic portfolio selection.Dynamics of Continuous,Discrete and Impulsive Systems,1998,(4):585-600
[41]Fama E F. Multi-period continuous-investment decisions. American Economic Review, 1970, (6): 163—174
[42]Nils H. Hakansson. Multi-period mean-variance analysis: Toward a general theory of portfolio choice. The Journal of Finance, 1971, 26(4):857—884
[43] Edwin J. Elton; Martin J. Gruber. On the optimality of some multiperiod portfolio selection criteria. The Journal of Business, 1974, 47 (2):231—243
[44]Merton RC. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 1971,(3):373—413
[45]Merton RC. Continuous-Time Finance. Cambridge: MA & Oxford, UK, 1990. 308-425
[46]Karatzas I, Wang H. Utility maximization with discretion ray stopping. Stamj Control and Optimization, 2000, 39(1):306-329
[47] Eugene W. Lambert, Alfred E. Hofflander, Impact of new multiple line underwriting on investment portfolios of property-liability insurers. The Journal of Risk and Insurance, 1966, 33 (2):209—223
[48]Krouse, Clement G, Portfolio balancing corporate assets and liabilities with special application to insurance management. The Journal of Financial and Quantitative Analysis, 1970, 5(1), 77—104
[49] Yehuda Kahane, David Nye. A portfolio approach to the property-liability insurance industry. Risk and Insurance, 1975,42(4):579—598
[50] Yehuda Kahane. Generation of investable funds and the portfolio behavior of the non-life insurance. The Journal of Risk and Insurance, 1978,45(1) :65—77
[51] Frost, A.J. Implications of modern portfolio theory for lift assurance companies. The Journal of the Institute of Actuaries, 1983, 26(1):47-68
[52]Petterson, J.A. The dependence of investment policy on the liabilities of a lift office. Transactions of the 22nd International Congress of Actuaries in Sydney, 1984, (15): 201-215