7 problems

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 $X$ be the surplus process, let $D$ be a dividend process, and let $R$ be a capital injection process in the optimization problem referenced as … Rt=-inf{sleq t}(Xs-Ds)wedge 0.…

Let $\mathbb{W}$ be the waiting region, let $\psi$ be the strictly increasing positive fundamental solution of the homogeneous differential equation, and let $R$ be a particular so…

Let $\mathcal{I}$ be the intervention region, let $\mathcal{L}_X$ be the infinitesimal generator of the exchange-rate process $X$, let $r$ be the discount rate, let $h$ be the runn…

Let $v$ denote the value function of the singular control problem, and let $w$ be an appropriate solution to the Hamilton–Jacobi–Bellman equation … where ${\mathcal L}_X$ is the op…