| Abstract: |
| Backwards SDEs (BSDEs) are object naturally arising in the pricing and hedging of financial derivatives, and have excited the interest of the mathematical community because of their deep connections with stochastic optimal control, PDEs, and their many applications, e.g. in game theory or economics. In this talk, we will first motivate BSDEs and then consider BSDE driven by general semimartingales in a unifying framework that allows to treat discrete- and continuous-time processes simultaneously. We will discuss general existence and uniqueness results, as well as stability results, i.e. convergence from discrete- to continuous-time BSDEs. Then, we will also consider mean-field and McKean-Vlasov BSDEs, discuss their existence and uniqueness theory, and also provide a novel proof for the backward propagation of chaos, i.e. the convergence of the mean-field BSDEs to the McKean-Vlasov limit. |
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