英文标题：
《Nonlinear Parabolic Equations arising in Mathematical Finance》
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作者：
Daniel Sevcovic
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最新提交年份：
2017
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英文摘要：
This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.
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中文摘要：
本文主要对金融数学中出现的抛物型全非线性偏微分方程进行定性和数值分析。主要目的是回顾用于金融工具定价的经典Black-Scholes理论的各种非线性扩展，以及导致Hamilton-Jacobi-Bellman（HJB）方程的随机动态投资组合优化模型。经过适当的变换，这两个问题都可以用非线性抛物方程的解来表示。定性分析将侧重于解决方案的存在性和唯一性问题。在数值部分，我们讨论了求解完全非线性抛物型方程的稳定有限体积和有限差分格式。
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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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