论文标题
在有限概率空间上的numéraire小扰动下的公平定价和对冲
Fair pricing and hedging under small perturbations of the numéraire on a finite probability space
论文作者
论文摘要
我们考虑了在Numéraire的小扰动下公平定价和对冲的问题。我们表明，对于可复制的主张，Numéraire的变化既不影响公平价格也不影响对冲策略。对于非复制主张，我们证明事实并非如此。通过以更容易的形式重新加以重新解决关键的随机控制问题，我们表明，对于Numéraire的小扰动，公平的价格和最佳策略都是稳定的。此外，我们的方法允许描述公平价格和对冲策略的领先订单校正条款的明确渐近公式。从数学上讲，我们的结果构成了在受控过程的集成商的某些扰动下对随机控制问题的稳定性和渐近分析，在这种情况下，约束使这个问题难以分析。
We consider the problem of fair pricing and hedging under small perturbations of the numéraire. We show that for replicable claims, the change of numéraire affects neither the fair price nor the hedging strategy. For non-replicable claims, we demonstrate that is not the case. By reformulating the key stochastic control problem in a more tractable form, we show that both the fair price and optimal strategy are stable with respect to small perturbations of the numéraire. Further, our approach allows for explicit asymptotic formulas describing the fair price and hedging strategy's leading order correction terms. Mathematically, our results constitute stability and asymptotic analysis of a stochastic control problem under certain perturbations of the integrator of the controlled process, where constraints make this problem hard to analyze.
