A note on optimal stopping of diffusions with a two-sided optimal rule

On the optimal stopping of a one-dimensional diffusion

“…Using martingale and change of measure techniques, Beibel and Lerche [5,6], Lerche and Urusov [26] and Christensen and Irle [10] developed an approach to determining an optimal stopping strategy at any given point in the interval I. Similar techniques have also been extensively used by Alvarez [1,2,3], Lempa [25] and references therein. To fix ideas, we consider the following representative cases that can be associated with any given initial condition x ∈ I.…”

Explicit solutions in one-sided optimal stopping problems for one-dimensional diffusions

“…The coefficients in (13) and (14) appeared (in a slightly different form) in Alvarez [2001], and also in Lempa [2010], and Lamberton and Zervos [2013].…”

“…The analysis of continuation intervals appears in Alvarez [2001] under restrictions on the shape of the continuation region. More recent references on one-sided and two-sided solutions are for instance Rüschendorf and Urusov [2008] and Lempa [2010]. Lamberton and Zervos [2013] obtain verification results in a framework of weak solutions of SDE with measurable coefficients and a state dependent discount.…”

Some results on optimal stopping under phase-type distributed implementation delay

“…On the other hand, if we assume that g is r -subharmonic on an interval (a, b), where 0 < a < b < ∞, then we would be likely to work out a set of assumptions such the resulting optimal continuation region is (z * , y * ), where 0 < z * < y * < ∞. These assumptions would most likely include boundedness and monotonicity assumptions of the functions g ψ r and g ϕ r , see Lempa (2010). However, this generalization is beyond the scope of this paper.…”