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math.PR2016
Exercising Control When Confronted by a (Brownian) Spider
Philip Ernst
We consider the Brownian "spider," a construct introduced in \cite{Dubins} and in \cite{Pitman}. In this note, the author proves the "spider" bounds by using the dynamic programmin…
q-fin.ST2016
On Optimal Retirement (How to Retire Early)
Philip Ernst, Dean Foster, Larry Shepp
We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function and our current net worth as for any , we invest…
q-fin.MF2016
Revisiting a Theorem of L.A. Shepp on Optimal Stopping
Philip Ernst, Larry Shepp
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…