6 problems

Constant-barrier conjecture. If the optimal strategy is of constant-barrier type, then the value function should have the form

Let $y_l<y_u$ be the critical distress thresholds, let $b^*_{r+q}<y_l<b^*(y_l)$, and let $a(y)$ and $\underline{b}(y)$ define the additional action component…

Let $y_l<y_u$ be the lower and upper critical distress thresholds, and let $\mathcal{D}^{y}$ denote the action region for distress threshold $y$. For $y otin (yl,yu)$, no additiona…

Additional-action-region conjecture. For $y>y_l$, there could be an additional action region around the point $b^*_{r+q}$. The subsequent section proves this conjectured phenomenon…

Let $w(x,i)$ be the value function when the surplus is $x$ and the Markov regime is $i\in\{1,2\}$. Let $d_1$ and $b_2$ satisfy $d_1<b_2$, and consider surplus levels…

Let $mu_1$ and $mu_2$ denote the drift parameters in regimes 1 and 2, respectively. The company starts with any surplus and may choose a dividend strategy, including liquidation by…