In this paper we consider stochastic optimization problems for a risk-avers investor when the decision maker is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary optimal stopping problems for one-dimensional Brow- nian motions we reduce the problem to the geometric problem of finding the smallest majorant of the reward function in an two-parameter function space. In a second part we solve optimal stopping problems when the underlying process can crash down. These problems are reduced to one optimal stopping problem and one Dynkin game. An explicit example is discussed.
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary optimal stopping problems for one-dimensional Brownian motions we reduce the problem to the geometric problem of finding the smallest majorant of the reward function in a two-parameter function space. In a second part we solve optimal stopping problems when the underlying process may crash down. These problems are reduced to one optimal stopping problem and one Dynkin game. Examples are discussed.
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An explicit example is
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