Stochastic control for a class of nonlinear kernels and applications
By Dylan Possamaï, Xiaolu Tan, Chao Zhou. 2015
67 citations recorded by the source corpus.
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalisations of the traditional (linear) expectations, this problem can be understood as stochastic control of a family of nonlinear expectations, or equivalently of nonlinear kernels. Our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting, which we then use to provide a semi-martingale characterisation of the value function. We next explore several applications of our results. We first obtain a wellposedness result for second order BSDEs (as introduced in [86]) which does not require any regularity assumption on the terminal condition and the generator. Then we prove a nonlinear optional decomposition in a robust setting, extending recent results of [71], which we then use to obtain a super-hedging duality in uncertain, incomplete and nonlinear financial markets. Finally, we relate, under additional regularity assumptions, the value function to a viscosity solution of an appropriate path-dependent partial differential equation (PPDE).
Subfields: Economics and Econometrics, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/ecddd2c73a6533d7daecc421bd1e40158423b2bf
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Citations in the corpus
- McKean–Vlasov optimal control: The dynamic programming principle (2019, result): “Similar results were obtained by several authors, among which we mention Nutz and Soner [63], Neufeld and Nutz [61; 62], Nutz and van Handel [64], Žitković [82], and Possamaï, Tan, and Zhou [68].”
- Mean–field moral hazard for optimal energy demand response management (2019, unknown): “First of all, the map 𝐹 can readily be rewritten as a function 𝐹(𝑥, 𝑦, (𝑆0)1∕2(𝑧1, 𝑧2)⊤, 𝑆0) as done by Possamaï, Tan, and Zhou (2018), since the matrix 𝑆0 is always invertible in our setting.”