On the LP formulation in measure spaces of optimal control problems for jump-diffusions

2015/04/13 by Rafael Serrano, Serrano, Rafael · 1 citation
Economics, Econometrics and Finance · Mathematics · Social Sciences · #35D40 #90C05 #93E20 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Insurance, Mortality, Demography, Risk Management #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:35D40 #msc:90C05 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1504.03392

openalex publication_date 2015/04/13 · arxiv created 2015/04/14 · arxiv updated 2015/04/15 · openalex created_date 2022/09/19 · openalex updated_date 2026/07/28

Abstract

In this short note we formulate a infinite-horizon stochastic optimal control problem for jump-diffusions of Ito-Levy type as a LP problem in a measure space, and prove that the optimal value functions of both problems coincide. The main tools are the dual formulation of the LP primal problem, which is strongly connected to the notion of sub-solution of the partial integro-differential equation of Hamilton-Jacobi-Bellman type associated with the optimal control problem, and the Krylov regularization method for viscosity solutions.

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