2016/04/13 by Erhan Bayraktar, Jiaqi Li, Bayraktar, Erhan +1
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Biology Tumor Growth #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1604.03906
openalex publication_date 2016/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we adapt stochastic Perron's method to analyze a stochastic target problem with unbounded controls in a jump diffusion set-up. With this method, we construct a viscosity sub-solution and super-solution to the associated Hamiltonian-Jacobi-Bellman (HJB) equations. Under comparison principles, uniqueness of the viscosity solutions holds and the value function coincides with the unique solution in the parabolic interior. Since classical control problems can be analyzed under the framework of stochastic target problems (with unbounded controls), we use our results to generalize the results in ArXiv:1212.2170 to problems with controlled jumps.