Expected Supremum Representation of the Value of a Singular Stochastic Control Problem

Abstract

We consider the problem of representing the value of singular stochastic control problems of linear diffusions as expected suprema. Setting the value accrued from following a standard reflection policy equal with the expected value of a unknown function at the running supremum of the underlying is shown to result into a functional equation from which the unknown function can be explicitly derived. We also consider the stopping problem associated with the considered singular stochastic control problem and present a similar representation as an expected supremum in terms of characteristics of the control problem.

22 pages, 1 figure

References in corpus (4)

• A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries
• Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance
• Impulse control and expected suprema
• Expected Supremum Representation and Optimal Stopping