英语翻译AbstractThis chapter introduces ordinary differential equation (ODE) and its applications in finance and economics research.There are various approaches to solve an ordinary differential equation.Among them,the most commonly used approach

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英语翻译AbstractThischapterintroducesordinarydifferentialequation(ODE)anditsapplicationsinfinanceandecon

英语翻译AbstractThis chapter introduces ordinary differential equation (ODE) and its applications in finance and economics research.There are various approaches to solve an ordinary differential equation.Among them,the most commonly used approach
英语翻译
Abstract
This chapter introduces ordinary differential equation (ODE) and its applications in finance and economics research.There are various approaches to solve an ordinary differential equation.Among them,the most commonly used approaches are the classical approach for a linear ODE and the Laplace transform approach.We demonstrate the applications of ODE in both deterministic and stochastic systems.As an application in deterministic systems,we apply ODE to solve a simple gross domestic product (GDP) model and an investment model of a firm,which is well studied in Gould (1968).As an application in stochastic systems,we employ ODE in a jump-diffusion model and derive the expected discounted penalty given the asset value follows a phase-type jump diffusion process.In particular,we study capital structure management model and derive the optimal default-triggering level.For related results,please see Chen etal.(2007).
Keywords:Default-triggering level,expected discounted penalty,investment model,Laplace transform,ordinary differential equation.
注：ODE为常微分方程

英语翻译AbstractThis chapter introduces ordinary differential equation (ODE) and its applications in finance and economics research.There are various approaches to solve an ordinary differential equation.Among them,the most commonly used approach
摘要：
这一章介绍常微分方程以及它在财经研究方面的应用.解决一个常微分方程有若干种方法.这些方法中最常用的方法是经典的线性常微分方程和拉普拉斯变换.我们展示的是常微分方程在确定性系统和随机性系统中的应用,我们用常微分方程解决简单的国民生产总值模型和公司投资模型,我们将常微分方程利用到跳跃-扩散模型中,得到了给定资产值的罚金折现期望随相形跳跃扩散的变化过程.特别的是,我们研究了资产结构管理模型并得出了理想的无力支付触发等级.相关结果请参照Chen等等（2007）
关键词：无力支付触发等级罚金折现期望投资模型拉普拉斯变换常微分方程
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文摘
本章所介绍的常微分方程(赋)及其在财经研究。有各种方法来解决常微分方程。其中,最常用的方法是最经典的方法为一个线性赋和拉普拉斯变换的方法。我们证明了他的应用两种结构的确定性和随机系统。作为一种应用》,我们运用确定性的系统来解决一个简单的国内生产总值(GDP)模型和投资模型对公司,主要研究了在-高德(1968)。作为一种应用在随机系统,我们雇用他服从跳跃-扩散模型和推导了点球将给贴...

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