An epsilon-minimum principle for multiobjective stochastic optimal control problems

In this paper we consider a multiobjective stochastic control problem and derive necessary conditions for approximate solutions of the control problem using a multicriteria variational principle of Ekeland's type. The restrictions in the multiobjective stochastic control problem are formulated by dynamical equations. The solution of these dynamical equations can be obtained applying the Girsanov measure transformation. Furthermore, the objective functions are terminal costs gi(x(1)) for which we consider the expected value of control u, i.e. Eu[gi(x(1))] = Fi(u) (i = 1,...,l) where Eu denotes the expectation constructed from control u.