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Insular grids are fragile owing to lower inertia and the absence of interconnection with other grids. With the increasing penetration of non-dispatchable renewable energy sources, the vulnerability of such insular grids increases further. The government of India has proposed several projects to improve the photovoltaic systems (PV) penetration in the Andaman and Nicobar Islands' grid. This paper investigates joint stochastic scheduling of energy and reserve generation for insular grids fed from diesel and gas-based generators, PV, and battery energy storage systems (BESS). The proposed stochastic scheduling model considers a wide range of probabilistic forecast scenarios instead of a deterministic model that assumes a single-point forecast. Hence, it provides an optimal solution that is technically feasible for a wide range of PV power forecast scenarios. The striking feature of the model developed in this work is the inclusion of stochastic constraints that represent (i) the coordination between PV and BESS, (ii) reserve constraints, (iii) battery charging/discharging limit constraints, and (iv) non-anticipatory constraints that ensure technical viability of scheduling decisions. The proposed model is validated on the dataset for South Andaman Island. Results reveal the applicability and feasibility of the proposed stochastic dispatch model for different generation mix scenarios. [ABSTRACT FROM AUTHOR]