Optimal decision under ambiguity for diffusion processes

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

Optimal stopping and hard terminal constraints applied to a missile guidance problem

This paper describes two new types of deterministic optimal stopping control problems: optimal stopping control with hard terminal constraints only and optimal stopping control with both minimum control effort And hard termind constraints. Both problems are initially formulated in continuous-time (a discretetime formulation is given towards the end of the paper) and soIutions given via dynamic programming. A numeric solution to the continuous-time dynamic programming equations is then briefly discussed. The optimal stopping with terminal constraints problem in continuous-time is a natural description of a particular type of missile guidance problem. This missile guidance appiication is introduced and the presented solutions used in missile engagements against targets