Revisiting a Theorem of L.A. Shepp on Optimal Stopping

Philip Ernst and Larry Shepp

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Abstract: Using a bondholder who seeks to determine when to sell his bond as our motivating example, we revisit one of Larry Shepp's classical theorems on optimal stopping. We offer a novel proof of Theorem 1 from from \cite{Shepp}. Our approach is that of guessing the optimal control function and proving its optimality with martingales. Without martingale theory one could hardly prove our guess to be correct.

Date: 2016-05
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Published in Communications on Stochastic Analysis (2015) 9(3): 419-423

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