2 research outputs found
A unified approach to well-posedness of type-I backward stochastic Volterra integral equations
We study a novel general class of multidimensional type-I backward stochastic
Volterra integral equations. Toward this goal, we introduce an infinite
dimensional system of standard backward SDEs and establish its well-posedness,
and we show that it is equivalent to that of a type-I backward stochastic
Volterra integral equation. We also establish a representation formula in terms
of non-linear semilinear partial differential equation of
Hamilton-Jacobi-Bellman type. As an application, we consider the study of
time-inconsistent stochastic control from a game-theoretic point of view. We
show the equivalence of two current approaches to this problem from both a
probabilistic and an analytic point of view