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摘要翻译：
在纯跳马尔可夫过程模型的不完全市场中，我们给出了二次套期保值策略的数值计算算法。利用Hamilton-Jacobi-Bellman方法，将二次套期保值问题的值函数转化为一个三角抛物型偏积分-微分方程组(PIDE)，并证明了PIDE在我们的背景下具有唯一的光滑解。第一个方程是非线性的，但不依赖于对冲期权的回报（纯投资问题），而另外两个方程是线性的。我们提出了收敛的有限差分格式来数值求解这些PIDE，并用电力市场的一个应用来说明我们的结果，在电力市场中，时间非齐次纯跳跃Markov过程以自然的方式出现。
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英文标题：
《Numerical methods for the quadratic hedging problem in Markov models
with jumps》
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作者：
Carmine De Franco, Peter Tankov and Xavier Warin
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最新提交年份：
2013
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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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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英文摘要：
We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem can be related to a triangular system of parabolic partial integro-differential equations (PIDE), which can be shown to possess unique smooth solutions in our setting. The first equation is non-linear, but does not depend on the pay-off of the option to hedge (the pure investment problem), while the other two equations are linear. We propose convergent finite difference schemes for the numerical solution of these PIDEs and illustrate our results with an application to electricity markets, where time-inhomogeneous pure jump Markov processes appear in a natural manner.
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PDF链接：
https://arxiv.org/pdf/1206.5393
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