7 problems

For a function $f:\mathbb{R}\mapsto\mathbb{R}$, define the impulse operator … Let ${\cal A}$ be the linear operator associated with the uncontrolled process $Y$, given for…

Player 2's quadratic value-function conjecture. We conjecture that $\Phi_2$ is quadratic in the state because the cost functions are quadratic in the state, and that

Multi-step optimal-policy conjecture. Similar results should hold for an $N$-step setup cost: some $(s,S)$ policies are optimal in some cases, whereas in other cases they can be do…

Let $D_2$ denote the continuation region for player II, and let $\hat{x}$ be a constant. Player II's continuation-region conjecture. The region $D_2$ is … This ansatz is used to ch…

Let $D_1$ denote the continuation region for player I, and let $\tilde{x}$ be a constant. Player I's continuation-region conjecture. The region $D_1$ is … This is an ansatz used to…

Let $X$ be a spectrally negative Lévy process, let $f$ be the holding cost function, and let $(d,D,U,u)$ be band-policy parameters. For an admissible policy $\pi=\{R^\pi,L^\pi\}$,…

In the impulse-control formulation, the intervention changes the reserve process by jumps; a band-type policy is described by intervention thresholds and post-intervention levels,…