Deterministic Minimax Impulse Control

Optimal investment and location decisions of a firm in a flood risk area using impulse control theory

“…Economic approaches are cost-effectiveness analyses, multi-criteria analyses, robust-decisionmaking approaches and dynamic programming (Zwaneveld and Verweij 2014;Eijgenraam et al 2012Eijgenraam et al , 2014. The most popular tool is cost-benefit analysis applied to cities (Lichfield 1960;Hunt and Watkiss 2011), regions, and countries [e.g.…”

The value of a minimax problem involving impulse control

“…Proof. The viscosity property follows from the dynamic programming principle and is proved in [17]. Now we give an equivalent of quasi-variational inequality (21).…”

“…In the finite horizon framework El Farouq et al [17] extended the work of Yong [28] but allowing general jumps. In this work the existence of the value functions of minimax impulse control problem and uniqueness of viscosity solution are obtained assuming that the dynamics and costs functionals are bounded and the impulse cost function should not depend on x.…”

“…Recently El Asri [13] have considered this minimax impulse control problem when the dynamics unbounded and cost functionals are bounded from below and the impulse cost function depends on x. In [13] and [17] the cost not less than α > 0, a near optimal strategy will never attempt to make an infinite number of jumps.…”

Deterministic minimax impulse control in finite horizon: the viscosity solution approach

“…Yong, in [9], also studies differential games where one person uses an impulse control and other uses continuous controls. Recently El Farouq et al [10] extended the work of Yong [21] in the finite horizon case but allowing general jumps. In all these works the existence of the value functions of optimal impulse control problem and uniqueness of viscosity solution are obtained assuming that the dynamics and costs functionals are bounded and the impulse cost function should not depend on y.…”