where c1, c2, c3, c4 are constants, B(s) is one dimensional Brownian motion and the
stochastic integral on the right hand side of (4) is in the sense of Itˆo (cf. [1]). In
that case φt1 (t) is actually a stochastic process φt1 (t, ω) and the problem of finding the
optimal switch-off time ˆ t1 now amounts to finding the first t1 for which