基于不同市场信息的套期保值策略研究

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3.0 陈辉 2024-11-19 6 4 991.15KB 147 页 15积分
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摘 要
本文针对套期保值这一金融风险管理问题进行了深入研究. 以投资者获取市
场信息多少为线索，在跳扩散风险资产价格模型下研究了未定权益的各种套期保
值策略. 通过构建不同的市场模型和市场信息结构，利用不同的
σ
-域充分刻画了
各种不同市场信息. 在此基础上依照模型特点选取不同的风险标准，在不同信息
条件下导出了最优投资策略. 更为具体的，论文针对完全信息、内部附加信息、
不完全信息和随机支付信息下的套期保值问题进行研究并解决了如下问题
●完全信息下的套期保值策略研究. 利用跳扩散模型来刻画风险资产的价
格过程，用布朗运动和泊松过程所生成的自然
σ
域来刻画投资者获得的所有信息.
首先通过构造一个辅助过程, 利用 Hilbert 空间投影定理给出了具体的均方套期
保值策略. 与以往的研究成果中最优策略(它往往含有与 Föllmer—Schweizer 分
解中的量，一般很难在实际中得到和应用) 相比, 它只涉及到市场可观测量, 具
有更好的应用价值；同时给出了完全信息下的亏损风险最小策略和风险最小套期
保值策略；
●内部附加信息下的套期保值策略研究. 通过构建内部信息市场模型，导出
了内部信息下的资产价格动态，首次解决了内部信息者的风险最小、亏损风险最
小和平方最优套期保值问题，给出了相应的最优策略的显式表示；
●不完全信息下套期保值策略研究. 基于风险资产价格动态的受价格外因
素影响和市场信息吸收率的季节依赖性的实际, 构建了双随机泊松跳扩散过程
及不完全信息市场模型. 然后在鞅方法的框架内给出两种不同情形下（无信息成
本和有信息成本）的风险最小套期保值策略；
● 随机支付信息下的套期保值策略研究. 通过引入 0-取得策略, 利用
Galtchouk-Kunita- Watanabee 分解和 Hilbert 空间中的投影定理将不完全信息下的
风险最小套期保值问题转化为一个闭子空间的投影问题, 从而证明了随机支付
信息下最优策略的存在性和唯一性， 给出了最优策略的可料投影表示. 首次成
功解决了不完全信息下的随机支付型未定权益的风险最小策略的选择问题, 得
到了最优策略的具体表示.
关键词：套期保值 市场信息 风险最小 亏损风险 信息成本 随
机支付 跳扩散模型
ABSTRACT
This dissertation studies deeply the research of hedging problem, which is an
important issue in financial risk management. With the amount of acquired market
information for investor as a clue, various hedging strategies are researched based on
jump-diffusion models. Through constructing market models and market information
structures, different market information is characterized as some -
σ
filtrations.
Various risk standards are selected according to the modes and some optimal portfolios
for different information are deduced. More specific, the hedging problems for complete
information, inner additional information, incomplete information and stochastic
payment information are studied and some problems as follows are resolved.
●The research of hedging strategies for complete information. Risky assets price
is modeled by a jump-diffusion process and all the obtained information for an investor
is characterized as the
σ
-filtration generated by Brownian motions and Poisson
processes. First, through constructing an auxiliary process, the specific
mean-variance hedging strategy is given using the project theorem in Hilbert space.
Compared with the existed results in which optimal strategies always contains
something coming from Föllmer-Schweizer decomposition and is not easy to be
acquired and applied in practice, the optimal strategy only consist of some observed
variable in the markets, and so has better value for practice; Also minimizing shortfall
risk strategies and risk-minimizing hedging strategies are obtained;
●The research of hedging strategies for inner additional information. By
constructing inner information market models, the dynamic of assets under inner
information is deduced. The problem of risk-minimizing, shortfall risk minimizing and
quadratic hedging strategies for the investors with inner information is solved. The
corresponding optimal hedging strategies are given explicitly.
●The research of hedging strategies for incomplete information. Based on the fact
that the price of risk assets is influenced by some factors out of the price and that market
information absorptivity is always affected by season a doubly stochastic Poisson jump-
diffusion process and an incomplete information market model is introduced. Then the
risk-minimizing hedging strategies in two different cases (i.e. free information costs and
information costs) are derived in the frame of martingale method.
●The research of hedging strategies for stochastic payments information. By the
definition of 0-achieving strategies, the problem of risk-minimizing hedging under
stochastic payments information is introduced. With Galtchouk-Kunita- Watanabee
decomposition and the risk minimizing hedging problem is converted to a projection
problem on a close subspace. And then the existence and uniqueness of the optimal
strategy under stochastic payments information is proved. The predictable projection
venison of the optimal strategy is given. The problem of risk-minimizing strategy
selection is solved for first time, and the concrete expression of the optimal policy is
derived.
Key Words: Hedging， Market information， Risk minimization,
Shortfall risk ， Information costs ， Stochastic payments ，
Jump-diffusion models
目 录
中文摘要
ABSTRCT
第一章 绪论 .................................................................................................................... 1
§1.1 课题来源及意义 ································································································1
§1.2 本文的研究目标和研究内容 ············································································3
§1.2.1 研究目标 ............................................................................................... 3
§1.2.2 研究内容 ............................................................................................... 4
§1.2.3 研究方法 ............................................................................................... 4
§1.3 本文的创新点····································································································6
§1.4 本文结构与章节安排 ························································································6
第二章 文献综述与基本理论 ........................................................................................ 9
§2.1 金融风险管理理论的发展 ·················································································9
§2.1.1 投资组合理论的发展 ........................................................................ 10
§2.1.2 套期保值理论的发展 ........................................................................ 14
§2.1.3 资产定价理论的发展 ........................................................................ 19
§2.1.4 金融工程理论的发展 ........................................................................ 22
§2.2 风险资产的价格行为与价格模型··································································· 23
§2.2.1 影响风险资产价格行为的因素 ........................................................ 23
§2.2.2 信息冲击与风险资产价格的跳行为 ................................................ 23
§2.2.3 风险资产的价格变化模型及评价 .................................................... 24
§2.3 一些预备知识·································································································· 29
§2.3.1 基本的数学概念和理论 ..................................................................... 30
§2.3.2 基本的数理金融知识 ......................................................................... 34
§2.3.3 跳扩散过程的一些预备知识 ............................................................. 35
§2.4 本章小结··········································································································· 37
第三章 完全信息下的套期保值策略研究 .................................................................. 39
§3.1 完全信息下的平方套期保值 ··········································································· 39
§3.1.1 完全信息下平方套期保值的研究现状 ............................................ 39
§3.1.2 基本市场模型和套期保值问题 ...................................................... 41
§3.1.3 平方最优套期保值策略的存在性及其表示 .................................... 43
§3.2 完全信息下亏损风险最小套期保值问题研究··············································· 49
§3.2.1 亏损风险最小套期保值问题及其研究现状 ..................................... 49
§3.2.2 价格模型及亏损风险最小问题的具体描述 ..................................... 50
§3.2.3 亏损风险最小策略的构建 ................................................................. 52
§3.3 完全信息下风险最小套期保值问题研究······················································· 54
§3.3.1 风险最小套期保值问题及其研究现状 ............................................. 54
§3.3.2 双随机跳扩散模型 ............................................................................ 55
§3.3.3 随机过程对 ()
tt
SX,的马尔可夫性 ................................................... 59
§3.3.4 完全信息下的风险最小套期保值策略 ............................................. 61
§3.4 本章小结·········································································································· 67
第四章 内部附加信息下的套期保值策略研究 .......................................................... 69
§4.1 内部信息市场风险管理问题的研究现状与方法 ············································ 69
§4.2 内部信息市场模型 ··························································································· 70
§4.3 内部附加信息下的风险最小套期保值策略···················································· 71
§4.4 内部信息市场的亏损风险最小问题································································ 75
§4.4.1 内部信息下亏损风险最小问题的提出 ............................................. 75
§4.4.2 内部信息者亏损风险最小策略问题的解 ......................................... 76
§4.4.3 一个简单的例子 ................................................................................. 84
§4.5 内部附加信息下的平方套期保值策略···························································· 88
§4.6 本章小结··········································································································· 92
第五章 不完全信息下的套期保值策略研究 .............................................................. 93
§5.1 不完全信息下的套期保值策略研究现状························································ 93
§5.2 价格模型假设··································································································· 94
§5.3 无信息成本下的风险最小套期保值策略······················································· 96
§5.3.1 价格模型特点 .................................................................................... 96
§5.3.2 不完全信息下风险最小套期保值策略 .......................................... 100
§5.4 有信息成本模型下的风险最小套期保值策略·············································· 103
§5.4.1 信息成本过程和有信息成本的金融市场 ....................................... 103
§5.4.2 有信息成本时完全信息下的风险最小套期保值策略 .................. 104
§5.4.3 有信息成本时不完全信息下的风险最小套期保值策略 ...............113
§5.5 本章小结········································································································ 114
第六章 随机支付信息下的套期保值策略研究 .........................................................117
§6.1 引言················································································································· 117
§6.2 随机支付模型与问题 ····················································································· 118
§6.3 完全信息下的风险最小套期策略································································· 121
§6.4 随机支付信息下的风险最小套期策略························································· 123
§6.5 本章小结········································································································· 128
第七章 结论与展望 .................................................................................................... 129
§7.1 结论················································································································ 129
§7.2 展望 ················································································································ 130
参考文献 ...................................................................................................................... 131
在读期间公开发表的论文和承担科研项目及取得成果 .......................................... 143
致 谢........................................................................................................................ 145
摘要：

摘要本文针对套期保值这一金融风险管理问题进行了深入研究.以投资者获取市场信息多少为线索，在跳扩散风险资产价格模型下研究了未定权益的各种套期保值策略.通过构建不同的市场模型和市场信息结构，利用不同的σ-域充分刻画了各种不同市场信息.在此基础上依照模型特点选取不同的风险标准，在不同信息条件下导出了最优投资策略.更为具体的，论文针对完全信息、内部附加信息、不完全信息和随机支付信息下的套期保值问题进行研究并解决了如下问题●完全信息下的套期保值策略研究.利用跳扩散模型来刻画风险资产的价格过程，用布朗运动和泊松过程所生成的自然σ域来刻画投资者获得的所有信息.首先通过构造一个辅助过程,利用Hilbert空间...

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