Vasily Belyaev

Vasily Belyaev is a Senior Associate at the Institute for Advanced Dynamic Uncertainty, where his work addresses stochastic optimal control in settings where the Markov property fails — problems in which the optimal decision at a given moment depends not only on the current state but on the full history of the system. He holds a PhD in Mathematics from Saint Petersburg State University (Faculty of Mathematics and Mechanics), where his doctoral research developed existence and uniqueness theory for backward stochastic differential equations with quadratic generators, and established their role in representing the value function of non-Markovian control problems via a stochastic version of the Pontryagin maximum principle.

Following his doctorate, Belyaev turned to the analysis of coupled forward-backward stochastic differential systems — the FBSDE framework that arises when the Pontryagin optimality conditions are written out as a coupled system for the state trajectory and the adjoint process. His work established well-posedness results for FBSDEs with non-Lipschitz coupling between the forward and backward components, and developed time-discretisation schemes in which the backward component is approximated through conditional expectation regressions on the forward trajectory. This numerical programme produced practical algorithms for a class of problems that lie beyond the reach of grid-based HJB methods.

At IADU, Belyaev applies the FBSDE framework to control and pricing problems in which path-dependence is intrinsic to the structure — instruments whose payoff depends on the full trajectory of a policy rate, sovereign contracts contingent on cumulative fiscal variables, or systems in which the diffusion coefficient itself carries memory. In these settings, the Hamilton–Jacobi–Bellman equation is inapplicable as stated, and the FBSDE representation of the value functional provides the correct analytical object from which optimal policies can be derived.