Conditional Essential Suprema with Applications

Conditional Essential Suprema with Applications,10.1007/s00245-003-0776-4,Applied Mathematics and Optimization,E. N. Barron,P. Cardaliaguet,R. Jensen

Conditional Essential Suprema with Applications   (Citations: 6)
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The conditional supremum of a random variable X on a probability space given a sub-s-algebra is defined and proved to exist as an application of the Radon–Nikodym theorem in L \infty. After developing some of its properties we use it to prove a new ergodic theorem showing that a time maximum is a space maximum. The concept of a maxingale is introduced and used to develop the new theory of optimal stopping in L \infty and the concept of an absolutely optimal stopping time. Finally, the conditional max is used to reformulate the optimal control of the worst-case value function.
Journal: Applied Mathematics and Optimization - APPL MATH OPT , vol. 48, no. 3, pp. 229-253, 2003
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