We consider a two-stage stochastic program with continuous recourse, where the distribution of the random parameters depends on the decisions. Assuming a finite sample space, we study a distributionally robust approach to this problem, where the decision-dependent distributional ambiguity is modeled with a polyhedral ambiguity set. We consider cases where the recourse function and the ambiguity set are either generic or have a special convex/nonconvex structure. We reformulate the resulting problem as a nonconvex two-stage stochastic program, including a bilinearly-constrained bilinear program and a concave minimization problem. We propose finitely-convergent decomposition-based cutting plane algorithms to solve the resulting problems optimally (or near-optimally). The proposed algorithm may also be used to solve two-stage stochastic programs with a random decision-dependent recourse matrix (i.e., bilinear stochasticity on the left-hand side) or a bilinear objective function. We illustrate computational comparative results for joint pricing and stocking decisions on a stylized multiproduct newsvendor problem with price-dependent demand.
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