... Doytchinov1
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, bd24@andrew.cmu.edu. 
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... Lehoczky2
Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, jpl@stat.cmu.edu. 
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... Shreve3
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213 shreve@cmu.edu. 
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