Abstract. In this talk, we study a structural compound stochastic program (SP) involving multiple expectations coupled by nonconvex and nondifferentiable functions. For solving the compound SP, we present a stochastic majorization-minimization (SMM) algorithm with incremental sampling scheme. We establish the almost sure subsequential convergence of the SMM algorithm to a fixed point of the algorithmic map. We relate such a point to several kinds of stationary solutions of the compound SP problem under different assumptions on the component functions. We further discuss probabilistic stopping rules based on the computable errorbound for the algorithm. We show several risk measure minimization problems that can be formulated as such a compound SP; these include generalized deviation optimization problems based on the optimized certainty equivalent and multi-class classification problems employing the cost-sensitive error criteria based on buffered probability of exceedance.