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

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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.