Optimal Impulse Control for Cash Management with Double Exponential Jump Diffusion Processes

Abstract

We consider a cash management problem where the cash demand is assumed to be double exponential jump-diffusion processes. We formulate a model minimizing the sum of the transaction and holding-penalty costs as an impulse control model. The model reduces to the problem of solving a Quasi-variational Inequality (QVI), and the function satisfying QVI is derived. We show that there is an optimal policy of the two-band type. Moreover, we discuss the effect of jumps on the optimal policy through some numerical examples.