英文标题：
《Analitic approach to solve a degenerate parabolic PDE for the Heston
model》
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作者：
A.Canale, R.M. Mininni, A.Rhandi
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最新提交年份：
2014
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英文摘要：
We present an analytic approach to solve a degenerate parabolic problem associated to the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We give a variational formulation, involving weighted Sobolev spaces, of the second order degenerate elliptic operator of the parabolic PDE. We use this approach to prove, under appropriate assumptions on some involved unknown parameters, the existence and uniqueness of weak solutions to the parabolic problem on unbounded subdomains of the half-plane.
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中文摘要：
我们提出了一种解析方法来解决与Heston模型相关的退化抛物线问题，该模型在数学金融中广泛用于推导随机波动风险资产上的欧式期权价格。我们给出了抛物型偏微分方程的二阶退化椭圆算子的一个包含加权Sobolev空间的变分公式。利用这种方法，在适当的假设条件下，证明了半平面无界子域上抛物问题弱解的存在唯一性。
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分类信息：

一级分类：Mathematics 数学
二级分类：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE\'s, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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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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