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摘要翻译：
基于一类带约束跳跃的倒向随机微分方程（简称BSDEs）的表示形式，提出了一种新的求解脉冲控制问题的概率方法。作为一个例子，我们的方法被用于摆动期权的定价。我们通过惩罚过程来处理跳跃约束，并将离散时间向后格式应用于所得到的惩罚的带跳跃的BSDE。我们研究了该数值方法对主要近似参数：跳跃强度λ、惩罚参数p>0和时间步长的收敛性。特别地，我们得到了由于惩罚阶$(\\lambdaP)^{\\alpha-\\frac{1}{2}}，\\\alpha\In\\left（0,\\frac{1}{2}\reght）$引起的误差的收敛速度。将该方法与蒙特卡罗方法相结合，在Black和Scholes框架下求解（规范化）摆动期权的估值问题。我们给出了数值试验，并与经典迭代法的结果进行了比较。
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英文标题：
《Swing Options Valuation: a BSDE with Constrained Jumps Approach》
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作者：
Marie Bernhart, Huy\^en Pham, Peter Tankov and Xavier Warin
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity $\lambda$, the penalization parameter $p > 0$ and the time step. In particular, we obtain a convergence rate of the error due to penalization of order $(\lambda p)^{\alpha - \frac{1}{2}}, \forall \alpha \in \left(0, \frac{1}{2}\right)$. Combining this approach with Monte Carlo techniques, we then work out the valuation problem of (normalized) Swing options in the Black and Scholes framework. We present numerical tests and compare our results with a classical iteration method.
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PDF链接：
https://arxiv.org/pdf/1101.0975
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