2013/11/27 by Gregor Heyne, Michael Kupper, Heyne, Gregor +5
Economics, Econometrics and Finance · Mathematics · #60H20 #60H30 #Economic theories and models #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1311.6910
openalex publication_date 2013/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study supersolutions of a backward stochastic differential equation, the control processes of which are constrained to be continuous semimartingales of the form dZ = Δdt + ΓdW. The generator may depend on the decomposition (Δ,Γ) and is assumed to be positive, jointly convex and lower semicontinuous, and to satisfy a superquadratic growth condition in Δ and Γ. We prove the existence of a supersolution that is minimal at time zero and derive stability properties of the non-linear operator that maps terminal conditions to the time zero value of this minimal supersolution such as monotone convergence, Fatou's lemma and L1-lower semicontinuity. Furthermore, we provide duality results within the present framework and thereby give conditions for the existence of solutions under constraints.