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On the optimal stopping problem for onedimensional diffusions, 2002. Working Paper (http://www.stat.columbia.edu/ ˜ik/DAYKAR.pdf
"... A new characterization of excessive functions for arbitrary one–dimensional regular diffusion processes is provided, using the notion of concavity. It is shown that excessivity is equivalent to concavity in some suitable generalized sense. This permits a characterization of the value function of the ..."
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Cited by 35 (2 self)
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A new characterization of excessive functions for arbitrary one–dimensional regular diffusion processes is provided, using the notion of concavity. It is shown that excessivity is equivalent to concavity in some suitable generalized sense. This permits a characterization of the value function of the optimal stopping problem as “the smallest nonnegative concave majorant of the reward function ” and allows us to generalize results of Dynkin and Yushkevich for standard Brownian motion. Moreover, we show how to reduce the discounted optimal stopping problems for an arbitrary diffusion process to an undiscounted optimal stopping problem for standard Brownian motion. The concavity of the value functions also leads to conclusions about their smoothness, thanks to the properties of concave functions. One is thus led to a new perspective and new facts about the principle of smooth–fit in the context of optimal stopping. The results are illustrated in detail on a number of non–trivial, concrete optimal stopping problems, both old and new.
Optimal stopping of linear diffusions with random discounting. Working paper, http://www.princeton.edu/ sdayanik/papers/additive.pdf
, 2003
"... Abstract. We propose a new solution method for optimal stopping problems for linear diffusions with random discounting. First, we extend the class of excessive functions for general diffusions and show that they are essentially concave. Then we use the new characterization of excessive functions to ..."
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Cited by 8 (3 self)
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Abstract. We propose a new solution method for optimal stopping problems for linear diffusions with random discounting. First, we extend the class of excessive functions for general diffusions and show that they are essentially concave. Then we use the new characterization of excessive functions to show that optimal stopping problems for linear diffusions discounted with respect to a continuous additive functional, recently studied by Beibel and Lerche [Theory Probab. Appl., 45(4):547–557, 2001], can be reduced to an undiscounted optimal stopping problem for standard Brownian motion. The latter problem can be solved essentially by inspection. The necessary and sufficient conditions for the existence of an optimal stopping rule are proved when the reward function is continuous. A proof of the smooth–fit principle is also provided. The results are illustrated on examples. 1.
ON THE CONVERGENCE FROM DISCRETE TO CONTINUOUS TIME IN AN OPTIMAL STOPPING PROBLEM 1
, 2005
"... We consider the problem of optimal stopping for a onedimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0, ∞], while the second class further restricts the set of allowed values ..."
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Cited by 3 (0 self)
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We consider the problem of optimal stopping for a onedimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0, ∞], while the second class further restricts the set of allowed values to the discrete grid {nh:n = 0,1,2,...,∞} for some parameter h> 0. The value functions for the two problems are denoted by V (x) and V h (x), respectively. We identify the rate of convergence of V h (x) to V (x) and the rate of convergence of the stopping regions, and provide simple formulas for the rate coefficients. 1. Introduction. One
The optimal Timing of Investment Decisions
 University of London
, 2006
"... discretionary stopping problem with applications to ..."
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discretionary stopping problem with applications to
time uncertainty
, 2007
"... This paper studies optimal stopping problems for general diffusion processes with an uncertain time horizon and with different levels of information based on which the decision to stop or to continue is made. First, corresponding value functions are compared and related explicitly to their counterp ..."
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This paper studies optimal stopping problems for general diffusion processes with an uncertain time horizon and with different levels of information based on which the decision to stop or to continue is made. First, corresponding value functions are compared and related explicitly to their counterparts without the time uncertainty. Second, to analyze optimal stopping strategies, characterization results regarding connectivity of the “stopping ” and “continuation ” regions are derived. In particular, sufficient conditions for the wellknown “threshold type ” optimal stopping rule are given, based on which explicit solutions are derived for problems with standard American call/put type payoff functions.