On the Impulse Control of Jump Diffusions

Regularity of the impulse control problem for a nondegenerate n-dimensional jump diffusion with infinite activity and finite variation jumps was recently examined in [M. H. A. Davis, X. Guo, and G. Wu, SIAM J. Control Optim., 48 (2010), pp. 5276–5293]. Here we extend the analysis to include infinite activity and infinite variation jumps. More specifically, we show that the value function u of the impulse control problem satisfies u ∈ Wloc2,p(Rn)

Asymptotics of impulse control problem with multiplicative reward

We consider a long-run impulse control problem for a generic Markov process with a multiplicative reward functional. We construct a solution to the associated Bellman equation and provide a verification result. The argument is based on the probabilistic properties of the underlying process combined with the Krein-Rutman theorem applied to the specific non-linear operator. Also, it utilises the approximation of the problem in the bounded domain and with the help of the dyadic time-grid

A Bank Salvage Model by Impulse Stochastic Controls

The present paper is devoted to the study of a bank salvage model with a finite time horizon that is subjected to stochastic impulse controls. In our model, the bank\u2019s default time is a completely inaccessible random quantity generating its own filtration, then reflecting the unpredictability of the event itself. In this framework the main goal is to minimize the total cost of the central controller, which can inject capitals to save the bank from default. We address the latter task, showing that the corresponding quasi-variational inequality (QVI) admits a unique viscosity solution\u2014Lipschitz continuous in space and H\uf6lder continuous in time. Furthermore, under mild assumptions on the dynamics the smooth-fit W(1,2),ploc property is achieved for any 1<+ 1e