-
摘要我国著名数学家彭实戈于上世纪 90 年代提出了一种典型的相容非线性数学期望——g-期望，该理论体系由倒向随机微分方程引入。与此同时，彭实戈指出g-期望满足经典数学期望的几乎所有性质，当然，线性性除外。此外，g-期望的许多性质都可以由一个满足确切性质的实函数来表述。 22290
- 上一篇：解析函数的无穷乘积分解及其应用
- 下一篇：SM2椭圆曲线公钥密码算法ECC研究与实现
风险测度的引入是为了定量分析和评估任意金融环境下的风险状况。伴随着风险测度理论的逐步发展，其局限性日益凸显。鉴于此，Artzner 提出了一致性风险测度，这一理论很快被广泛接受。随后，弱化一致性风险测度中的正齐次性和次可加性公理， 便可以得到更为符合实际经济环境的风险测度——凸性风险测度。 近年来，g-期望理论无论是在金融数学还是在数理经济学等领域的应用都已经越来越广泛，如用于金融市场的未定权益定价、风险测度等。2003年，Rosazza Giani 提出由g-期望可以构造一致性风险测度。由此，众多学者都着手研究g-期望跟风险测度之间的联系。
本论文首先介绍了 g-期望、风险测度、一致性风险测度、凸性风险测度的相关知识，然后将 g-期望与风险测度理论结合，研究了基于 g-期望的两类风险测度的表示定理。
毕业论文关键词： g-期望 风险测度 基于g-期望的风险测度
Title The Essential Character of Risk Measure via g-Expectation and Application
Abstract
In the 1990s,the mathematician of our country, Shige Peng introduced a
typical filtration consistent nonlinear expectation—g-expectation by the
theory of the Backward Stochastic Differential Equations. In the meantime,
Peng said that g-expectation satisfies all properties of the classical
mathematical expectation besides the linearity. In addition ,the
g-expectation is uniquely specified by a real function which satisfying
certain properties.
Risk measures were introduced to quantify the risk of any financial
position. With the development of the theory of risk measures, its
limitation becomes increasingly prominent. For this reason, Artzner
proposed the coherent risk measures and this theory was soon widely
accepted. Subsequently, we can get a risk measure which is more suitable
for the actual economic environment—convex risk measures by weakening the
positive homogeneity and the subadditivity of coherent risk measures.
In recent years, the application of g-expectation has become
increasingly widespread in the field of financial mathematics and
mathematical economics. It has been applied to the pricing of contingent
claims in the financial market, as well as to risk measures. 2003, Rosazza
Giani proposed that g-expectation can construct the coherent risk
measures. Thus, many scholars began to study the connection between the
g-expectation and the risk measures.
This paper first introduced the knowledge of the g-expectation, risk measures, coherent risk measures, convex risk measures, then combine the
g-expectation with the theory of risk measures and study the risk measures
via g-expectation.
Keywords: g-expectation risk measures risk measures via
g-expectation
目 次
1 绪论… 1
1.1 g-期望的提出与发展… 1
1.2 风险测度的提出与发展 1
1.3 g-期望与风险测度 2
1.4 本文章节安排 2
2 经典数学期望与 g-期望 4