摘要翻译:
根据经典鞅表示定理,随机向量的复制可以通过随机积分或随机微分方程的解来实现。我们引入了一种新的方法,通过由受控常微分方程产生的自适应可微过程来复制随机向量。我们发现这个复制问题的解决方案是存在的,并且不是唯一的。这就引出了一个新的最优控制问题:寻找一个在积分范数中最小的复制过程。我们找到了这个问题的明确解决方案。建议了在证券组合选择问题和债券定价模型中的可能应用。
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英文标题:
《Optimal replication of random claims by ordinary integrals with
applications in finance》
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作者:
Nikolai Dokuchaev
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最新提交年份:
2013
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分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Portfolio Management 项目组合管理
分类描述:Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类:Mathematics 数学
二级分类:Optimization and Control 优化与控制
分类描述:Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学,线性规划,控制论,系统论,最优控制,博弈论
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英文摘要:
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable processes generated by a controlled ordinary differential equation. We found that the solution of this replication problem exists and is not unique. This leads to a new optimal control problem: find a replicating process that is minimal in an integral norm. We found an explicit solution of this problem. Possible applications to portfolio selection problems and to bond pricing models are suggested.
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PDF链接:
https://arxiv.org/pdf/1301.0381