Abstract: Systems, apparatuses, methods, and computer program products are disclosed for determining a value corresponding to a composite object. Paths are determined based on initial values of underlying items of the composite object and random numbers. A DNN is trained by determining a final value for each path based on a final set of items corresponding to the path at the final time, iterating the value backward in time using a non-linear generator function from the final value to an initial value, defining a set of initial values comprising the initial value determined for each path and determining a statistical measure based on the set of initial values, and modifying parameters of the DNN based on the statistical measure. Value information comprising the value for the composite object at one or more times is determined based on output of the DNN. The value information is provided such that a user computing device receives it.

Abstract: Systems, apparatuses, methods, and computer program products are disclosed for determining and providing value information and/or boundary activation information for a system defined in an at least partially bounded domain (i.e., the boundary of said domain consisting of at least one point) and having boundary conditions imposed at a boundary thereof. A deep BSDE solver is trained by, for each time step and for each path, determining, based on a set of underlying features for that path, whether a boundary condition has been activated for the path. When it is determined that a boundary condition has been activated for a first time for the path, an output value for the path is updated based on the boundary condition, an output time is updated based on the boundary activation time step, and not updated further. When the boundary condition was not activated for the path by the final time, the output value for the path is a final corresponding value.