Risk-sensitive stochastic control and its singular limit

风险敏感随机控制及其奇异极限

基本信息

  • 批准号:
    10440030
  • 负责人:
  • 金额:
    $ 3.33万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (B).
  • 财政年份:
    1998
  • 资助国家:
    日本
  • 起止时间:
    1998 至 2000
  • 项目状态:
    已结题

项目摘要

(a) It is important to know the conditions for no breakdown in risk-sensitive stochastic control problems since the value function has not always a finite value. In this research we have obtained the condition as that of the size of risk-sensitive parameter in the case of a finite time horizon and also shown the solvability of the corresponding Bellman equation under the condition. It is applicable for the case that the risk-sensitive parameter is large and has great meaning in application. In the case of infinite time horizon we have shown existence and uniqueness of the corresponding ergodic type Bellman equation under a similar condition by noticing the relationships between the problems and the eigenvalue problems for Schrodinger operator. Besides, we have derived a first order partial differential equation relating to game theoretical approach to nonlinear H_∞ control as its singular limit.(b) We have considered portfolio optimization problem for a factor model as application to m … More athematical finance of risk-sensitive stochastic control and got the results giving the explicit representation to optimal portfolio for the problem in the case of partial information. In the case of infinite time horizon we obtained the condition under which the solution of corresponding ergodic type Bellman equation defines the optimal portfolio and constructed it by the solution. We have also found that the solution does not always give the optimal portfolio without any condition.(c) We have shown existence of the spectral gap of Schrodinger opeartor by using log Sobolev inequality and gave the estimate.(d) We have shown that the large deviation principle holds for additive functional of Brownian motion corresponding to measures in Kato class. As its application we obtained necessary and sufficient condition under which additive functionals converges exponentially fast.(e) We have shown Trotter product formula with respect to L_p and trace norm and their error estimates for the Schrodinger operator with a potential bounded below.(f) We have shown that the sequence of symmetric statistics defined by Weyl transformation on infinite dimensional torus converges to the limit represented by multiple Wiener integral under the probability measures. Less
(a)在风险敏感随机控制问题中,由于值函数并不总是有限值,因此了解不崩溃的条件是很重要的。本文得到了有限时间水平下风险敏感参数大小的条件,并证明了相应的Bellman方程在该条件下的可解性。该方法适用于风险敏感参数较大的情况,具有重要的应用意义。在无限时域情形下,通过注意问题与Schrodinger算子特征值问题之间的关系,我们证明了相应的遍历型Bellman方程在类似条件下的存在唯一性.此外,我们还导出了一个与非线性H_∞控制的对策论方法有关的一阶偏微分方程作为其奇异极限。(b)我们考虑了一个因素模型的投资组合优化问题,作为对M ...更多信息 风险敏感随机控制的数学金融问题,得到了部分信息情况下最优投资组合的显式表示。在无限时间范围的情形下,得到了相应的各态历经型Bellman方程的解定义最优投资组合的条件,并利用该解构造了最优投资组合。我们还发现,解决方案并不总是给最优的投资组合没有任何条件。(c)利用对数Sobolev不等式证明了薛定谔算符谱隙的存在性,并给出了估计。(d)证明了布朗运动的可加泛函对应于Kato类中的测度时,大偏差原理成立。作为应用,我们得到了可加泛函指数快速收敛的充要条件。(e)本文给出了位势有界的Schrodinger算子关于L_p和迹模的Trotter乘积公式及其误差估计。(f)证明了无穷维环面上由Weyl变换定义的对称统计量序列在概率测度下收敛于由多重Wiener积分表示的极限。少

项目成果

期刊论文数量(122)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
M. Takeda: "Exponential decay of lifetime and a theorem of Kac on total occupation times"Potential Analysis. 11. 235-247 (1999)
M. Takeda:“寿命的指数衰减和 Kac 关于总占用时间的定理”潜力分析。
  • DOI:
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    0
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S.Aida: "Precise Gaussian lower bounds on heat kernels"in "Stochastics in Finite and Infinite Dimensions, In bonor of Gopinath Kallianpur, " Birkhauser.. 1-28. (2000)
S.Aida:“热核的精确高斯下界”,载于“有限和无限维度的随机指标”,Gopinath Kallianpur 的博诺尔,“Birkhauser.. 1-28。
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    0
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M.Takeda: "Topics on Dirichlet forms and symmetric Markov processes"Sugaku Expositions. 12. 201-222 (1999)
M.Takeda:“关于狄利克雷形式和对称马尔可夫过程的主题”Sugaku Expositions。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
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A,Bensoussan,J.Frehse and H.Nagai: "Some Results on Risk-sensitive Contint with Full Obserration" Applied Mathematics and its Optimization. 37. 1-41 (1998)
A,Bensoussan,J.Frehse 和 H.Nagai:“风险敏感连续性充分观察的一些结果”应用数学及其优化。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
J.Sekine: "Information Geometry for Symmetric Diffusions"Potential Analysis. 1-30 (2001)
J.Sekine:“对称扩散的信息几何”潜力分析。
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  • 影响因子:
    0
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NAGAI Hideo其他文献

NAGAI Hideo的其他文献

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{{ truncateString('NAGAI Hideo', 18)}}的其他基金

Stochastic control on a long term and its applications
长期随机控制及其应用
  • 批准号:
    25400150
  • 财政年份:
    2013
  • 资助金额:
    $ 3.33万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Development of the methods of stochastic control and filtering in mathematical finance
数学金融中随机控制和过滤方法的发展
  • 批准号:
    20340019
  • 财政年份:
    2008
  • 资助金额:
    $ 3.33万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
BELLMAN EQUATIONS OF RISK-SENRSITIVE STOCHASTIC AND THEIR APPLICATIONS
风险敏感随机贝尔曼方程及其应用
  • 批准号:
    13440033
  • 财政年份:
    2001
  • 资助金额:
    $ 3.33万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Histochemical and genetic study of cystic tumors of the pancreas
胰腺囊性肿瘤的组织化学和遗传学研究
  • 批准号:
    12671254
  • 财政年份:
    2000
  • 资助金额:
    $ 3.33万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
The molecular and clinicopathological study related to detection of K-ras point mutation in the blood of pancreatic cancer cases
胰腺癌患者血液中K-ras点突变检测相关的分子及临床病理学研究
  • 批准号:
    08671480
  • 财政年份:
    1996
  • 资助金额:
    $ 3.33万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Nuclear DNA analysis of genetics of cancer and dysplasia complicating ulcerative colitis
癌症和溃疡性结肠炎并发不典型增生的遗传学核 DNA 分析
  • 批准号:
    62570593
  • 财政年份:
    1987
  • 资助金额:
    $ 3.33万
  • 项目类别:
    Grant-in-Aid for General Scientific Research (C)
Nationl Unification Thriugh the Modern emperor System
通过现代皇帝制度实现国家统一
  • 批准号:
    61450045
  • 财政年份:
    1986
  • 资助金额:
    $ 3.33万
  • 项目类别:
    Grant-in-Aid for General Scientific Research (B)
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