论文标题
在不完整的市场中最佳对冲
Optimal Hedging in Incomplete Markets
论文作者
论文摘要
我们认为，在不完整的市场中，具有既定定价内核的最佳对冲问题。在这样的市场中，价格是唯一确定的，但通常不可用。我们在相当普遍的环境中工作，在莱维 - 伊托（Lévy-Ito）市场的环境中，资产是由$ n $维的布朗尼运动共同驱动的，并且在$ n $二维状态空间上进行了独立的泊松随机度量。鉴于需要对冲的位置和作为对冲的仪器，我们证明了最佳的对冲投资组合的存在，其中通过在指定的时间范围内使用预期最小二乘正方形的标准来定义最佳性，而在其中，将套被视为与Benchmark相关的套罩的工艺与指定的kernel相关。
We consider the problem of optimal hedging in an incomplete market with an established pricing kernel. In such a market, prices are uniquely determined, but perfect hedges are usually not available. We work in the rather general setting of a Lévy-Ito market, where assets are driven jointly by an $n$-dimensional Brownian motion and an independent Poisson random measure on an $n$-dimensional state space. Given a position in need of hedging and the instruments available as hedges, we demonstrate the existence of an optimal hedge portfolio, where optimality is defined by use of an expected least squared-error criterion over a specified time frame, and where the numeraire with respect to which the hedge is optimized is taken to be the benchmark process associated with the designated pricing kernel.
