Efficient

Efficient 1:8μm KTiOPO 4optical parametric oscillator pumped within an Nd:YAG =SrWO 4Raman laser

Fen Bai,1,2Qingpu Wang,1,2Zhaojun Liu,1,2,*Xingyu Zhang,1,2Wenjia Sun,1,2

Xuebin Wan,1,2Ping Li,1,2Guofan Jin,1and Huaijin Zhang 3

1

School of Information Science and Engineering,Shandong University,Jinan,Shandong 250100,China

2

Shandong Provincial Key Laboratory of Laser Technology and Application,

Shandong University,Jinan,Shandong 250100,China

3

Institute of Crystal Materials,Shandong University,Jinan,Shandong 250100,China

*Corresponding author:zhaojunliu@https://www.sodocs.net/doc/ef11212588.html,

Received September 23,2010;revised January 21,2011;accepted January 25,2011;

posted February 1,2011(Doc.ID 135511);published March 8,

2011

A 1:8μm optical parametric oscillator (OPO)based on a noncritically phase-matched KTiOPO 4crystal is demon-strated.OPO and stimulated Raman scattering techniques are successfully combined in an acousto-optically Q -switched Nd:YAG =SrWO 4Raman laser.The device efficiently realizes three steps of conversion:from a laser diode wavelength of 808nm to the fundamental wavelength of 1064nm ;next,to the Stokes wavelength of 1180nm ;and finally to the OPO signal wavelength of 1810nm .With an incident diode power of 7:2W and a pulse repetition rate of 15kHz ,an average signal power of 485mW is obtained with a diode-to-signal conversion efficiency of 6.75%.The beam quality factors (M 2)of the signal wave in both horizontal and vertical directions are measured to be 1:7?0:2.The numerical output power results of the system,the thermal lensing,and the stability parameter of the cavity are also discussed.?2011Optical Society of America OCIS codes:190.4410,190.4970,140.3550.

An optical parametric oscillator (OPO)is a popular efficient nonlinear frequency conversion technique for generating new laser lines based on a second-order non-linear effect [1–3].Stimulated Raman scattering (SRS)is another well-known method for frequency conversion based on a third-order nonlinear optical process [4–6].OPO in combination with SRS provides a promising way for extending the wavelength range,because both OPO and SRS are flexible and efficient for generating di-verse laser wavelengths.Therefore,combining OPO with SRS is of great significance and is expected to find appli-cations where existing laser systems cannot be effective.We attempt to implement this combination by using Raman radiation to pump an OPO.An OPO can operate only above the oscillating threshold,so the pump radia-tion must be intensive enough to reach the threshold.Moreover,the lower-order laser transverse modes gener-ate the OPO output more efficiently than the higher-order ones [2].Therefore,the pump radiation should have good beam quality for efficient conversion.Solid-state Raman lasers based on the SRS effect satisfy both requirements.First,the Raman laser has been proven to be a good source for generating high-efficiency and high-power Stokes waves [4–6].Second,owing to the beam cleanup effect of SRS [7],the beam quality of the Raman radiation is improved significantly over that of the pump beam.Therefore,it is suggested that one use the Raman radia-tion to generate high-power radiation with good beam quality for pumping an OPO,without any additional beam-shaping elements.To our knowledge,using the Raman laser to pump an OPO is a novel approach.In this Letter,a KTiOPO 4(KTP)intracavity IOPO pumped by an acousto-optically (AO)Q -switched diode-pumped Nd:YAG =SrWO 4Raman laser is demonstrated.A SrWO 4crystal is chosen as the Raman crystal for its high Raman gain and good thermal and mechanical properties [8].A KTP crystal is employed as the OPO crystal and cut for Type II noncritically phase-matched (NCPM)config-uration for the maximum effective nonlinear coefficient and acceptance angle.The 1064nm radiation from the Nd:YAG crystal is Stokes-shifted to a 1180nm laser in the SrWO 4crystal.The 1180nm Raman laser acts as the pumping source for the KTP-OPO,from which the 1810nm signal wave is obtained.At an incident laser diode (LD)power of 7:2W and a pulse repetition rate (PRR)of 15kHz,a signal output power of 485mW is achieved The diode-to-signal conversion efficiency is 6.75%.The beam quality factors (M 2)are 1:7?0:2in both horizontal and vertical directions.

The experimental configuration of the KTP-OPO pumped within the Nd:YAG =SrWO 4Raman laser is shown in Fig.1.Both the fundamental and OPO cavities were inside the Raman cavity.A fiber-coupled 808nm LD (25W,NA ?0:22,d core ?600μm)was used as the pump-ing source.The gain medium was an Nd:YAG rod (1:0at :%Nd-doped,?4mm ×10mm).The Raman active

Fig.1.(Color online)Optical configuration of the KTP-IOPO pumped by Nd:YAG =SrWO 4Raman laser.LD,laser diode;RM,rear mirror;OC,output coupler;AO,acousto-optical Q -switch;KTP,KTiOPO 4crystal;HR,high reflection;HT,high transmis-sion;AR,antireflection;PR,partial reflection.March 15,2011/Vol.36,No.6/OPTICS LETTERS 813

0146-9592/11/060813-03$15.00/0

?2011Optical Society of America

medium was an A-cut SrWO 4crystal with dimensions of 3:7mm ×3:7mm ×33:9mm.Both faces of Nd:YAG and SrWO 4were coated for high transmission at 1064and 1180nm (T >99:8%).A Type II NCPM KTP crystal (X-cut,θ?90°,??0°)with a size of 3mm ×3mm ×30mm was employed as the OPO crystal.Both faces were anti-reflective (AR)coated at 1810and 1180nm (R <0:2%).The 35mm-long AO Q -switch (Gooch &Housego,USA)had AR coatings (R <0:2%)at 1064nm on both faces and was driven at 41MHz center frequency with 15W of rf power.All the crystals were wrapped with indium foil and mounted in water-cooled copper blocks.The water temperature was maintained at 20°C.The cavity lengths of the fundamental,Raman,and OPO cavities were 115,165,and 43mm,respectively.

Before studying the OPO characteristics,another out-put coupler (OC)with a reflection of 90%at 1180nm and low reflection at 1810nm was used to investigate the per-formance of the Nd:YAG =SrWO 4Raman laser.We placed the KTP crystal and the second mirror (M2)inside the laser cavity without the OPO functioning.The highest diode-to-Stokes conversion efficiency of 19.9%was ob-tained with an output power of 1:4W at a pump power of 6:8W and a PRR of 15kHz.The Raman pulse width was measured to be 22ns under the same conditions.Figure 2shows the average output power at 1180nm with respect to the pump power for PRRs of 12.5,15,and 17:5kHz.The Raman output saturated and declined be-cause of the thermally induced instability when pump power was higher than certain values.In addition,the output saturated at a lower pump power for lower PRR because at lower PRR the thermal problem was more ser-ious and self-focusing-induced damage could occur [5,6].We measured the M 2values for 1180and 1064nm beams at the Stokes output power of 1:4W.A NanoScan beam analyzer (Photon,Inc.,USA)and CCD (Duma Optronics Ltd,Israel)were used to study the M 2values for 1180and 1064nm beams,respectively.The M 2values for 1064nm were measured to be 5:2?0:2(horizontal)and 5:7?0:2(vertical),while for 1180nm,they were 1:9?0:2(hori-zontal)and 2:1?0:2(vertical).The beam quality of the Raman laser was much better than the fundamental wave,which is consistent with the Raman cleanup effect.

When the OC designed for OPO operation was used,we investigated the output characteristics of the KTP-OPO pumped within the Nd:YAG =SrWO 4Raman laser.We first studied the spectral characteristics of the output signal wave.The signal spectral information was moni-tored with a spectral analyzer system.The measured result is shown in Fig.3.The signal wavelength was de-termined to be 1810?1nm.The idler wave at around 3390nm was strongly absorbed by the KTP crystal and the cavity mirrors (BK7glass).As a result,we did not observe the idler wave in our experiment.

Figure 4shows the average output power at 1810nm with respect to the pump power for PRRs of 12.5,15,and 17:5kHz.With the pump power increased,the trend of OPO output was similar to that of Raman output because the signal was generated from the depleted Raman field.At lower PRRs,the threshold for OPO operation could be reduced because more population inversions were accu-mulated.Furthermore,this threshold was less than 4:6W at the PRR of 12:5kHz.The maximum signal output power of 485mW was obtained at a pump power of 7:2W and a PRR of 15kHz,corresponding to a diode-to-signal conversion efficiency of 6.75%.When measuring the 1810nm pulse widths,the pulse-series phenomenon [3]was observed at higher pump powers.At the highest sig-nal output power,the pulse width of an 1810nm laser pulse was measured to be 2:7ns and the peak power was up to 12kW.It should be noticed that the value of the signal pulse width was for the first (or main)pulse of the pulse series.We also studied the beam quality for the 1810nm signal and 1180nm Raman beams (at the highest signal output power of 485mW).The Nano-Scan beam analyzer and the CCD mentioned above were used to study the M 2values of the signal and the Raman waves,respectively.The M 2values for the 1810nm beam were determined to be 1:7?0:2in both horizontal and vertical directions.The M 2values for an 1180nm beam were 5:1?0:2and 5:5?0:2in the horizontal and vertical directions,respectively.The beam quality was improved after the parametric process.

The numerical output power results were calculated based on rate equations derived by combining the Raman theory [9]and the OPO theory [10].The results are de-picted as lines in Figs.2and 4.Although the numerical results are in agreement with the experimental results on the whole,some discrepancies can also be observed at lower and higher pump powers.The reasons may

be

Fig.2.(Color online)Average output power at 1180nm with respect to the pump power for PRRs of 12.5,15,and 17:5kHz.Symbols,experimental results;lines,numerical

results.

Fig.3.Optical spectrum of the signal wave at 1810nm.

814OPTICS LETTERS /Vol.36,No.6/March 15,2011

as follows:first,the thermal effects impact some param-eters (e.g.,beam cross sections and diffraction losses)used in the calculation.The changes of these parameters with respect to the pump power were not taken into account.Second,we approximate that the lasers are in TEM 00mode,which is actually not very accurate at higher pump powers.

At the highest signal output power of 485mW,using the method in [6],the equivalent thermal focal lengths of Nd:YAG,SrWO 4,and KTP were estimated to be 250,2000,and 230mm,respectively.From the results,we can see the thermal effect of SrWO 4crystal was relatively slight.This may be attributed to the homogeneous heat distribution inside the Raman medium during the scatter-ing process.The thermal effect of Nd:YAG and KTP were much more serious.The serious thermal effect of Nd:YAG is mainly due to high quantum defect and the nonuniform pumping of the LD end pump scheme.The serious thermal effect of KTP is probably due to the strong absorption at idler wave and the small Raman beam spot radius inside the KTP crystal (estimated to be 0:16mm by the ABCD matrix).

Based on these focal lengths,the value of the j A tD j =2parameter,which indicates the stability of the cavity,was also calculated at the same condition.It was 0.390,0.451,and 0.999for the fundamental,signal,and Raman waves,respectively.These values reveal that although the funda-mental and OPO cavities were quite stable,the Raman cavity was critically stable when the signal output reached the highest value.Therefore,the difficulty in generating higher 1810nm output power mainly lies in the limited stable zone of the Raman wave.Besides the thermal lens effect and the self-focusing effect,long Raman cavity length is also a critical issue to the Raman cavity stability in our experiment.To overcome this pro-blem,it is suggested that the Raman cavity length be shortened {e.g.,by inserting a mirror [high reflection (HR)for 1180nm and AR for 1064nm]between the

AO and the SrWO 4crystal},which is left for future work.In addition,if one mirror coated for HR at 1064nm and AR at 1180nm on one surface and HR at 1810nm and AR at 1180nm on the other surface is available,we can sub-stitute this mirror to for the two mirrors (M1and M2in this experiment).This is also expected to scale up the 1810nm output.

In conclusion,the combination of OPO and SRS has been realized by using a Raman laser to pump an intra-cavity OPO.The laser source comprised an AO Q -switched Nd:YAG module that produced 1064nm fun-damental radiation,an SrWO 4Raman crystal that gener-ated a first Stokes laser at 1180nm,and a KTP crystal that generated a parametric signal wave at 1810nm.The three steps of conversions from the LD wavelength to the OPO signal wavelength have been efficiently realized.The conversion efficiency was 6.75%from the input diode power of 7:2W to the signal output power of 485mW.The peak power was up to 12kW.The M 2factors of the signal wave in both horizontal and vertical directions were 1:7?0:2.We also have discussed the numerical output power results of the system,the thermal lensing,and the stability parameters of the cavity.Therefore,it is feasible to use SRS radiation to pump an NCPM OPO.Ex-tending this idea to other schemes,such as SRS pumping a critically phase-matched OPO,is also possible for pur-sing coherent laser sources at new wavelength regions.This work was supported by the National Natural Science Foundation of China (NSFC),Nos.60677027and 60908010;by the Science and Technology Development Program of Shandong Province,No.2007GG10001026;and by the China Postdoctoral Science Foundation,No.20090451301.

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Fig.4.(Color online)Average output power at 1810nm with respect to the pump power for PRRs of 12.5,15,and 17:5kHz.Symbols,experimental results;lines,numerical results.

March 15,2011/Vol.36,No.6/OPTICS LETTERS 815

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Chapter 6 Are Financial Markets Efficient? Multiple Choice Questions 1. How expectations are formed is important because expectations influence (a) the demand for assets. (b) bond prices. (c) the risk structure of interest rates. (d) the term structure of interest rates. (e) all of the above. Answer: E 2. According to the efficient market hypothesis, the current price of a financial security (a) is the discounted net present value of future interest payments. (b) is determined by the highest successful bidder. (c) fully reflects all available relevant information. (d) is a result of none of the above. Answer: C 3. The efficient market hypothesis (a) is based on the assumption that prices of securities fully reflect all available information. (b) holds that the expected return on a security equals the equilibrium return. (c) both (a) and (b). (d) neither (a) nor (b). Answer: C 4. If the optimal forecast of the return on a security exceeds the equilibrium return, then (a) the market is inefficient. (b) an unexploited profit opportunity exists. (c) the market is in equilibrium. (d) only (a) and (b) of the above are true. (e) only (b) and (c) of the above are true. Answer: D

Efficient Capital Markets- A Review of Theory and Empirical Work-Fama,JF(有效市场假设EMH)

Classical Works in Financial Economics Eugene F. Fama 效率资本市场：理论与实证研究评述 效率资本市场：理论和实证研究评述Eugene F. Fama 金融经济学名著译丛『第 1 页』 效率资本市场：理论与实证研究评述* Eugene F. Fama+ 原载《金融学杂志》，1970 年5 月，第25 卷第2 册，第383-417 页 1、引言 资本市场的主要作用是配臵经济体中资本存量的所有权。总的来讲，在理想 市场中，价格提供了准确的资源配臵信号：也就是一个企业能够做出生产——投资决策，以及在假定任何时期的证券价格都―完全反映‖了可得信息的前提下，投资者能够在代表企业经营所有权的证券之间进行选择的市场。一个价格总是能够―完全反映‖可得信息的市场被称为是―有效率的‖。 本文对效率市场模型的理论和实证研究进行了评述。在对有关理论进行研讨 之后，考察了关于证券价格对三个相关信息子集调整的实证研究。首先，讨论了弱形式检验，在该形式下，信息集为历史价格。接下来，考察了半强形式检验，重点放在价格是否对其他公开披露的信息（如公布年度盈利、股票拆细等）做出有效调整。最后，评述了强形式检验，侧重于既定的投资者或群体是否单独拥有与价格形成有关的任何信息1。我们的结论是：除去少数例外情况，效率市场模型成立得相当好。 尽管我们采用从理论到实证研究的方法，从历史观点来看，我们注意到该领 域的实证研究在很大程度上领先于理论的发展。这里给出的理论主要是为了便于判断哪些实证结果从理论观点来看更加具有关联性。然而，我们或多或少地依照历史序列的方式对实证研究本身进行评述。 最后，细心的读者会发现在本文的有些地方没有对相关的研究进行专题讨 论。我对此表示抱歉：该领域的文献浩如烟海，有所取舍是必然的。不过，只要梳理出效率市场研究的主线，并准确地描述该领域当前的进展状况，也就达到了本文的主要目标。 * 本研究项目由国家科学基金提供资助。我对Arthur Laffer，Robert Aliber，Ray Ball，Micheal Jensen，James Lorie，Merton Miller，Charles Nelson，Richard Roll，William Talor 和Ross Watts 提出的意见表示感谢。 + 现就职于Chicago 大学和计量经济学协会。 1 弱形式和强形式检验之间的区别首先由Harry Roberts 提出。 效率资本市场：理论和实证研究评述Eugene F. Fama 金融经济学名著译丛『第 2 页』 2、效率市场理论 2.1 期望回报或“公平游戏”模型

Efficient

Efficient 1:8μm KTiOPO 4optical parametric oscillator pumped within an Nd:YAG =SrWO 4Raman laser Fen Bai,1,2Qingpu Wang,1,2Zhaojun Liu,1,2,*Xingyu Zhang,1,2Wenjia Sun,1,2 Xuebin Wan,1,2Ping Li,1,2Guofan Jin,1and Huaijin Zhang 3 1 School of Information Science and Engineering,Shandong University,Jinan,Shandong 250100,China 2 Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University,Jinan,Shandong 250100,China 3 Institute of Crystal Materials,Shandong University,Jinan,Shandong 250100,China *Corresponding author:zhaojunliu@https://www.sodocs.net/doc/ef11212588.html, Received September 23,2010;revised January 21,2011;accepted January 25,2011; posted February 1,2011(Doc.ID 135511);published March 8, 2011 A 1:8μm optical parametric oscillator (OPO)based on a noncritically phase-matched KTiOPO 4crystal is demon-strated.OPO and stimulated Raman scattering techniques are successfully combined in an acousto-optically Q -switched Nd:YAG =SrWO 4Raman laser.The device efficiently realizes three steps of conversion:from a laser diode wavelength of 808nm to the fundamental wavelength of 1064nm ;next,to the Stokes wavelength of 1180nm ;and finally to the OPO signal wavelength of 1810nm .With an incident diode power of 7:2W and a pulse repetition rate of 15kHz ,an average signal power of 485mW is obtained with a diode-to-signal conversion efficiency of 6.75%.The beam quality factors (M 2)of the signal wave in both horizontal and vertical directions are measured to be 1:7?0:2.The numerical output power results of the system,the thermal lensing,and the stability parameter of the cavity are also discussed.?2011Optical Society of America OCIS codes:190.4410,190.4970,140.3550. An optical parametric oscillator (OPO)is a popular efficient nonlinear frequency conversion technique for generating new laser lines based on a second-order non-linear effect [1–3].Stimulated Raman scattering (SRS)is another well-known method for frequency conversion based on a third-order nonlinear optical process [4–6].OPO in combination with SRS provides a promising way for extending the wavelength range,because both OPO and SRS are flexible and efficient for generating di-verse laser wavelengths.Therefore,combining OPO with SRS is of great significance and is expected to find appli-cations where existing laser systems cannot be effective.We attempt to implement this combination by using Raman radiation to pump an OPO.An OPO can operate only above the oscillating threshold,so the pump radia-tion must be intensive enough to reach the threshold.Moreover,the lower-order laser transverse modes gener-ate the OPO output more efficiently than the higher-order ones [2].Therefore,the pump radiation should have good beam quality for efficient conversion.Solid-state Raman lasers based on the SRS effect satisfy both requirements.First,the Raman laser has been proven to be a good source for generating high-efficiency and high-power Stokes waves [4–6].Second,owing to the beam cleanup effect of SRS [7],the beam quality of the Raman radiation is improved significantly over that of the pump beam.Therefore,it is suggested that one use the Raman radia-tion to generate high-power radiation with good beam quality for pumping an OPO,without any additional beam-shaping elements.To our knowledge,using the Raman laser to pump an OPO is a novel approach.In this Letter,a KTiOPO 4(KTP)intracavity IOPO pumped by an acousto-optically (AO)Q -switched diode-pumped Nd:YAG =SrWO 4Raman laser is demonstrated.A SrWO 4crystal is chosen as the Raman crystal for its high Raman gain and good thermal and mechanical properties [8].A KTP crystal is employed as the OPO crystal and cut for Type II noncritically phase-matched (NCPM)config-uration for the maximum effective nonlinear coefficient and acceptance angle.The 1064nm radiation from the Nd:YAG crystal is Stokes-shifted to a 1180nm laser in the SrWO 4crystal.The 1180nm Raman laser acts as the pumping source for the KTP-OPO,from which the 1810nm signal wave is obtained.At an incident laser diode (LD)power of 7:2W and a pulse repetition rate (PRR)of 15kHz,a signal output power of 485mW is achieved The diode-to-signal conversion efficiency is 6.75%.The beam quality factors (M 2)are 1:7?0:2in both horizontal and vertical directions. The experimental configuration of the KTP-OPO pumped within the Nd:YAG =SrWO 4Raman laser is shown in Fig.1.Both the fundamental and OPO cavities were inside the Raman cavity.A fiber-coupled 808nm LD (25W,NA ?0:22,d core ?600μm)was used as the pump-ing source.The gain medium was an Nd:YAG rod (1:0at :%Nd-doped,?4mm ×10mm).The Raman active Fig.1.(Color online)Optical configuration of the KTP-IOPO pumped by Nd:YAG =SrWO 4Raman laser.LD,laser diode;RM,rear mirror;OC,output coupler;AO,acousto-optical Q -switch;KTP,KTiOPO 4crystal;HR,high reflection;HT,high transmis-sion;AR,antireflection;PR,partial reflection.March 15,2011/Vol.36,No.6/OPTICS LETTERS 813 0146-9592/11/060813-03$15.00/0 ?2011Optical Society of America

金融经济学-名词解释

确定性：是指自然状态如何出现已知，并替换行动所产生的结果已知。它排除了任何随机事件发生的可能性。 风险：是指那些涉及已知概率或可能性形式出现的随机问题，但排除了未数量化的不确定性问题。即对于未来可能发生的所有事件，以及每一事件发生的概率有准确的认 识。但对于哪一种事件会发生却事先一无所知。 不确定性：是指发生结果尚未不知的所有情形，也即那些决策的结果明显地依赖于不能由决策者控制的事件，并且仅在做出决策后，决策者才知道其决策结果的一类问题。即知道未来世界的可能状态（结果），但对于每一种状态发生的概率不清楚。 自然状态：特定的会影响个体行为的所有外部环境因素。 自然状态的特征：自然状态集合是完全的、相互排斥的（即有且只有一种状态发生） 自然状态的信念（belief）：个体会对每一种状态的出现赋予一个主观的判断，即某一特定状态s出现的概率P（s）满足：0≤p（s）≤1，这里的概率p（s）就是一个主观概率，也成为个体对自然的信念。不同个体可能会对自然状态持有不同的信念，但我们通常假定所有的个体的信念相同，这样特定状态出现的概率就是唯一的。 数学期望最大化原则：数学期望收益最大化准则是指使用不确定性下各种可能行为结果的预期值比较各种行动方案优劣。这一准则有其合理性，它可以对各种行为方案进行准确的优劣比较，同时这一准则还是收益最大准则在不确定情形下的推广。 期望效用原则：指出人们在投资决策时不是用“钱的数学期望”来作为决策准则，而是用“道德期望”来行动的。而道德期望并不与得利多少成正比，而与初始财富有关。穷人与富人对于财富增加的边际效用是不一样的。即人们关心的是最终财富的效用，而不是财富的价值量，而且，财富增加所带来的边际效用（货币的边际效用）是递减的。 效用函数的表述和定义：不确定性下的选择问题是其效用最大化的决定不仅对自己行动的选择，也取决于自然状态本身的选择或随机变化。因此不确定下的选择对象被人们称为彩票（Lottery）或未定商品（contingent commodity。 不确定性下的偏好关系表述：个体所有可选择抽奖的集合称为抽奖空间，记为：L=（p，x，y）同样地，假设个体在抽奖空间上存在一个偏好关系，即可以根据自己的标准为所有抽奖排出一个优劣顺序。 公理1： 公理2： 公理3 公平博彩是：指不改变个体当前期望收益的赌局，如一个博彩的随机收益为，其期望收益为，我们就称其为公平博彩。 风险厌恶者：如果经济主体拒绝接受公平博彩，这说明该个体在确定性收益和博彩之间更偏好确定性收益，我们称该主体为风险厌恶者。 风险偏好者：如果一个经济主体在任何时候都愿意接受公平博彩，则称该主体为风险偏好者。定义：u是经济主体的VNM效用函数，W为个体的初始禀赋，如果对于任何满足E（3-）=0，var（3-）〉0的随机变量3-，有u（W）〉E[u(W+3-)]，则称个体是（严格）风险厌恶（risk aversion）；如果上述不等号方向相反，则称个体是风险偏好（risk loving）；如果两边相等，则称个体是风险中性（neutral） 确定性等价值（certainty equivalence）：是指经济行为主体对于某一博彩行为的支付意愿。即与某一博彩行为的期望效用所对应的数学期望值（财富价值）。 风险溢价（risk premium）：是指风险厌恶者为避免承担风险而愿意放弃的投资收益。或让一个风险厌恶的投资者参与一项博彩所必需获得的风险补偿。 风险溢价与最优资产组合选择定理（绝对风险厌恶系数）：如果一个经济主体是严格风险厌