Research on pricing theory in incomplete financial markets by using stochastic analysis

我已经完成了对差额风险度量的研究，这些度量出现在关于良好交易范围的研究中。差额风险度量是代表最低价格的凸性风险度量，它使卖家能够通过选择合适的套期保值策略来抑制低于其限额的差额风险。在2010财年上半年，我将2009财年得到的结果推广到标的资产价格过程是非局部有界的情形，并成功地在锥约束和凸约束下得到了一些结果。此外，在后半部分，我研究了逆卷积，并将其应用于缺口风险度量问题。结果，虽然我只得到了作为Orlicz空间一部分的Orlicz心的结果，但我成功地将其推广到一般的Orlicz空间。

I have completed my research on shortfall risk measures which appear in research on good deal bounds. Shortfall risk measures are convex risk measures representing the least price which enables a seller selling a claim to suppress her shortfall risk less than her limitation by selecting a suitable hedging strategy. Shortfall risk measures would decide candidates of prices of contingent claims.In the first half of FY 2010, I extended results which I had obtained in FY 2009 to the case where the underlying asset price process is non-locally bounded, and succeeded in getting some results on models under cone and convex constraints. Moreover, in the second half, I studied inf-convolutions, and applied it to the shortfall risk measure problem. As a result, while I had obtained results only on Orlicz hearts which are parts of Orlicz spaces, I succeeded in extending to general Orlicz spaces.