基于几何分析的风险调整定价方法模型研究
Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis
摘要：
一族的精确解被发现的非线性修改的Black-Scholes方程。这种风险调整定价方法模型（RAPM）结合了交易成本和波动性投资组合的风险。利用李群分析得到了RAPM方程所允许的李代数。它给我们的可能性来描述一个最佳系统的子代数和相应的一套不变的解决方案的模型。通过这种方式，我们可以描述非线性RAPM模型的可能约简的完整集合。降阶以不同的二阶常微分方程的形式给出。在所有情况下，我们提供的解决方案，这些方程的精确或参数的形式。我们讨论这些减少和相应的不变解的性质。
英文摘要：
Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and correspondingly the set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide solutions to these equations in an exact or parametric form. We discuss the properties of these reductions and the corresponding invariant solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
