Optimal replication of random vectors by ordinary integrals

We consider a problem of replication of random vectors by ordinary integrals in the setting when an underlying random variable is generated by a Wiener process. The goal is to find an optimal adapted process such that its cumulative integral at a fixed terminal time matches this variable. The optimal process has to be minimal in an integral norm.

► Optimal replication of random vectors by ordinary integrals is considered.
► Possibility of exact match is established.
► Optimal solution is suggested.