时滞倒向随机微分方程的应用 至定价、对冲及投资组合管理

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摘要翻译：
本文研究一类新的方程组&时滞倒向随机微分方程的新应用。在金融学中，当我们要寻找一个投资策略和一个投资组合时，时滞BSDEs可能会出现，该投资策略和投资组合应该根据所应用的策略或投资组合的过去价值来复制一个负债或满足一个目标。在这种情况下，管理的投资组合既是负债/目标所依赖的基础证券，又是该负债/目标的复制组合。对于资本保护型投资和与业绩挂钩的回报而言，通常都是如此。我们给出了可以在时滞BSDES框架下研究的定价、套期保值和投资组合管理问题（资产负债管理问题）的例子。我们的动机来自人寿保险，我们专注于参与合同和可变年金。我们导出了相应的时滞BSDEs，并显式地求解它们，或者至少提供了如何数值求解它们的提示。我们对时滞BSDE可能没有解或可能有多个解这一理论事实给出了金融解释。
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英文标题：
《Applications of time-delayed backward stochastic differential equations
  to pricing, hedging and portfolio management》
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作者：
Lukasz Delong
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最新提交年份：
2011
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  In this paper we investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in finance when we want to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the applied strategy or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability/target is contingent and as a replicating portfolio for that liability/target. This is usually the case for capital-protected investments and performance-linked pay-offs. We give examples of pricing, hedging and portfolio management problems (asset-liability management problems) which could be investigated in the framework of time-delayed BSDEs. Our motivation comes from life insurance and we focus on participating contracts and variable annuities. We derive the corresponding time-delayed BSDEs and solve them explicitly or at least provide hints how to solve them numerically. We give a financial interpretation of the theoretical fact that a time-delayed BSDE may not have a solution or may have multiple solutions.
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PDF链接：
https://arxiv.org/pdf/1005.4417

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关键词：倒向随机微分方程 随机微分方程 投资组合管理 组合管理 投资组合 复制 负债 equations 可能 定价