Minimizing or maximizing the first-passage time to a time-dependent boundary. (1st February 2022) - Lefebvre, Mario
Abstract : Let X ( t ) be a one-dimensional controlled diffusion process, and Y ( t ) be a deterministic process. Various models are considered for ( X ˙ ( t ), Y ˙ ( t ) ) . The optimizer tries to bring the ratio X ( t ) / Y ( t ) to a certain value d as soon as possible. There is also a second optimizer whose aim is to prevent the ratio X ( t ) / Y ( t ) 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.