Ship collision accidents are rare events but pose huge threat to human lives, assets, and the environment. Collision resistance of ships is usually assessed in terms of ship structural response such as member displacement, energy dissipation and the extent of damage. Many researchers have sought for effective models that compute ship stochastic response during collisions by considering the variability of collision scenario parameters. However, the models were limited by the capability of the collision computational models and did not completely capture collision scenario, and material and geometric uncertainties. In addition, the simplified models capturing the input-response relationships of the ship structural impact mechanics are in implicit forms which makes them unsuitable for assessing the performance of structural design specifications in collisions. Furthermore, with increasing ship passages in the Arctic region, the probabilities of ship-iceberg interactions are increasing, highlighting the need to focus on risk based ship designs. In this research, a conceptual stochastic modelling framework is developed for performance characterisation and quantitative risk assessment of ship-ship and ship-iceberg collisions. In this direction, an interface for automated stochastic finite element computations was developed to model ship structural resistance in reference collision scenarios. The stochastic structural response was characterised based on the onset of the ship structural failure. The focus was initially on ship-ship collisions to quantify the uncertainties experimentally and to characterise the performance for a variety of striking ships. The framework was then extended to consider probabilistic performance measures in ship-iceberg collisions. The computationally intensive collision response models were captured with efficient surrogate representations so that the performance measures can be obtained with gradient based reliability approaches. The most probable input design sets for the response distribution were sampled with Latin Hypercube models. The probabilistic performance measures were also combined with available collision frequency models from literature for risk computations and to demonstrate the risk tolerance measures. The framework underlines the significance of different risk components, providing valuable guidance for improving risk-based ship designs. Although, a double-hull crude oil carrier is presented as the struck ship, the approach can be readily extended to characterise the performance and risk of other ship structures in collisions.