论文标题
与迭代积分和神经网络混乱的对冲
Chaotic Hedging with Iterated Integrals and Neural Networks
论文作者
论文摘要
在本文中，我们基于迭代的Stratonovich积分来得出$ l^p $ -CHAOS扩展，相对于给定的指数性连续连续的Semimartingale。通过省略扩展的正交性，我们表明，可以通过有限的迭代stratonovich积分来近似[1，\ infty）$ in [1，\ infty）$ in [1，\ infty）$的$ p \。使用（可能是随机）神经网络作为集成，我们在$ l^p $ sense中获得了$ p $积分金融衍生品的通用近似结果。此外，我们可以大致解决$ l^p $ - hedging问题（恰好与二次对冲问题相吻合），在此，可以在短期运行时以封闭形式计算近似的对冲策略。
In this paper, we derive an $L^p$-chaos expansion based on iterated Stratonovich integrals with respect to a given exponentially integrable continuous semimartingale. By omitting the orthogonality of the expansion, we show that every $p$-integrable functional, $p \in [1,\infty)$, can be approximated by a finite sum of iterated Stratonovich integrals. Using (possibly random) neural networks as integrands, we therefere obtain universal approximation results for $p$-integrable financial derivatives in the $L^p$-sense. Moreover, we can approximately solve the $L^p$-hedging problem (coinciding for $p = 2$ with the quadratic hedging problem), where the approximating hedging strategy can be computed in closed form within short runtime.
