2021/11/18 by Tiziano De Angelis, De Angelis, Tiziano, Alessandro Milazzo +1 · 1 citation
Economics, Econometrics and Finance · #49L20 #60G07 #60G40 #93E20 #Climate Change Policy and Economics #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2111.09608
openalex publication_date 2021/11/18 · openalex created_date 2022/10/27 · openalex updated_date 2026/07/28
We prove the dynamic programming principle (DPP) in a class of problems where\nan agent controls a d-dimensional diffusive dynamics via both classical and\nsingular controls and, moreover, is able to terminate the optimisation at a\ntime of her choosing, prior to a given maturity. The time-horizon of the\nproblem is random and it is the smallest between a fixed terminal time and the\nfirst exit time of the state dynamics from a Borel set. We consider both the\ncases in which the total available fuel for the singular control is either\nbounded or unbounded. We build upon existing proofs of DPP and extend results\navailable in the traditional literature on singular control (e.g., Haussmann\nand Suo, SIAM J. Control Optim., 33, 1995) by relaxing some key assumptions and\nincluding the discretionary stopping feature. We also connect with more general\nversions of the DPP (e.g., Bouchard and Touzi, SIAM J. Control Optim., 49,\n2011) by showing in detail how our class of problems meets the abstract\nrequirements therein.\n