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摘要翻译：
我们研究了Schoenbucher和Wilmott，2000年提出的非流动性市场中自筹资金交易策略的一般模型。在此模型框架下，套期保值策略满足一个非线性偏微分方程(PDE)，该方程含有函数g(alpha)。这个函数与效用函数有很深的联系。我们描述了该偏微分方程的Lie对称代数，并给出了该偏微分方程到常微分方程的一组完备的约简。此外，我们还能够描述所有类型的函数g(alpha)，其PDE允许一个扩展李群。三个特殊类型函数中的两个导致了不同作者以前介绍的模型，一个是新的。我们阐明了这三个特殊模型与非流动性市场交易策略的一般模型之间的联系。我们用李群分析法研究了PDE描述自筹资金策略的新特例。在一般模型和新的特殊模型中，我们都给出了子代数的最优系统，并研究了偏微分方程到不同ODE的完备约简集。在所有情况下，我们都能够提供新的特殊模型的显式解。在其中一种情况下，解描述了幂导数产品。
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英文标题：
《Models of self-financing hedging strategies in illiquid markets:
symmetry reductions and exact solutions》
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作者：
Ljudmila A. Bordag, Anna Mikaelyan
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最新提交年份：
2010
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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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英文摘要：
We study the general model of self-financing trading strategies in illiquid markets introduced by Schoenbucher and Wilmott, 2000. A hedging strategy in the framework of this model satisfies a nonlinear partial differential equation (PDE) which contains some function g(alpha). This function is deep connected to an utility function. We describe the Lie symmetry algebra of this PDE and provide a complete set of reductions of the PDE to ordinary differential equations (ODEs). In addition we are able to describe all types of functions g(alpha) for which the PDE admits an extended Lie group. Two of three special type functions lead to models introduced before by different authors, one is new. We clarify the connection between these three special models and the general model for trading strategies in illiquid markets. We study with the Lie group analysis the new special case of the PDE describing the self-financing strategies. In both, the general model and the new special model, we provide the optimal systems of subalgebras and study the complete set of reductions of the PDEs to different ODEs. In all cases we are able to provide explicit solutions to the new special model. In one of the cases the solutions describe power derivative products.
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PDF链接：
https://arxiv.org/pdf/1008.2663
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