2025/07/02 by Dylan Possamaï, Possamaï, Dylan, Marco Rodrigues +3
Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Risk and Portfolio Optimization #Economic theories and models
paper · pdf · doi:10.48550/arxiv.2507.01767
We construct an aggregated version of the value processes associated with stochastic control problems, where the criterion to optimise is given by solutions to semi-martingale backward stochastic differential equations (BSDEs). The results can be applied to control problems where the triplet of semi-martingale characteristics is controlled in a possibly non-dominated case or where uncertainty about the characteristics is present in the optimisation. The construction also provides a time-consistent system of fully nonlinear conditional expectations on the Skorokhod space. We find the semi-martingale decomposition of the value function and characterise it as the solution to a semi-martingale second-order BSDE. The generality we seek allows for the treatment of controlled diffusions, pure-jump processes, and discrete-time processes in a unified setting.