Potential theory in optimal stopping and alternatinc processes

2005 ◽  
pp. 285-293
Author(s):  
Jean-Michel Bismut
Keyword(s):  
Potential Theory ◽  
Optimal Stopping

Optimal stopping of constrained Brownian motion

1972 ◽  
Vol 9 (3) ◽  
pp. 557-571 ◽  
Author(s):  
Hans Föllmer
Keyword(s):  
Brownian Motion ◽  
Potential Theory ◽  
Optimal Stopping ◽  
Optimal Strategy ◽  
Critical Value ◽  
Standard Process ◽  
Reward Function

We discuss the potential theory of optimal stopping for a standard process and an unbounded reward function. This is applied to Brownian motion constrained to a N(m, σ2) distribution at time 1. Boyce [2] has discovered, via computer, various interesting features of this example. We provide direct proofs for some of them, in particular for the qualitative jump of the optimal strategy as the variance σ2 passes the critical value 1.

Optimal stopping of constrained Brownian motion

1972 ◽  
Vol 9 (03) ◽  
pp. 557-571
Author(s):  
Hans Föllmer
Keyword(s):  
Brownian Motion ◽  
Potential Theory ◽  
Optimal Stopping ◽  
Optimal Strategy ◽  
Critical Value ◽  
Standard Process ◽  
Reward Function

We discuss the potential theory of optimal stopping for a standard process and an unbounded reward function. This is applied to Brownian motion constrained to aN(m,σ2) distribution at time 1. Boyce [2] has discovered, via computer, various interesting features of this example. We provide direct proofs for some of them, in particular for the qualitative jump of the optimal strategy as the varianceσ2passes the critical value 1.

Potential Theory and Right Processes

2004 ◽  
Author(s):  
Lucian Beznea ◽  
Nicu Boboc
Keyword(s):  
Potential Theory

Optimal Stopping Time for Geometric Random Walks with Power Payoff Function

2020 ◽  
Vol 81 (7) ◽  
pp. 1192-1210
Author(s):  
O.V. Zverev ◽  
V.M. Khametov ◽  
E.A. Shelemekh
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Payoff Function ◽  
Optimal Stopping Time
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