Let be a one-dimensional controlled diffusion process, and be a deterministic process. Various models are considered for . The optimizer tries to bring the ratio to a certain value d… Click to show full abstract
Let be a one-dimensional controlled diffusion process, and be a deterministic process. Various models are considered for . The optimizer tries to bring the ratio to a certain value d as soon as possible. There is also a second optimizer whose aim is to prevent the ratio from reaching d as long as possible. Explicit solutions are obtained. The particular case when the control variables are assumed to be constants and the general case are treated.
               
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