In this paper we extend the stability results of [4]}. Our utility maximization problem is defined as an essential supremum of conditional expectations of the terminal values of wealth processes, conditioned on the filtration at the stopping time \tau. The stability result , in particular, implies that in the framework of 4 , the optimal wealth at any given stopping time is stable with respect to changes in the Sharpe ratio and initial wealth. To establish our results, we extend the classical results of convex analysis to maps from L^0 to L^0. The notion of convex compactness introduced in [7] plays an important role in our analysis.
In this paper we extend the stability results of [4]}. Our utility maximization problem is defined as an essential supremum of conditional expectations of the terminal values of wealth processes, conditioned on the filtration at the stopping time \tau. As a corollary, the stability result implies that in the framework of \mbox{%DIFAUXCMD MR2438002 , the optimal wealth at any given stopping time is stable with respect to changes in the Sharpe ratio and initial wealth. To establish our results, we extend the classical results of convex analysis to maps from L^0 to L^0. The notion of convex compactness introduced in [7] plays an important role in our analysis.
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The stability result , in particular,
As a corollary, the stability result
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\mbox{%DIFAUXCMD MR2438002