Smooth solutions to discounted reward control problems with unbounded discount rate and financial applications

2016/02/02 by Dariusz Zawisza, Zawisza, Dariusz
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR) #math.OC #math.PR #q-fin.MF

paper · pdf · doi:10.48550/arxiv.1602.00899

arxiv created 2016/02/16 · arxiv updated 2016/02/17

Abstract

We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a smooth classical solution to the corresponding HJB equation. Moreover, some verification reasoning are provided and the possible extension to dynamic games is discussed. At the end of the paper consumption - investment problems arising in financial economics are considered.

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