The variation of and the interrelation between different energy markets significantly affect the competitiveness of various energy technologies, therefore complicate the decision-making problem for a complex energy system consisting of multiple competing technologies, especially in a long-term time frame. The interrelations between these markets have not been accounted for in the existing energy system modelling efforts, leading to a distortion of understanding of the market impact on the technological choices and operations in the real world. This study investigates the strategic and operational decision-making problem for such an energy system characterized by three competing technologies from crude oil, natural gas, and coal. A stochastic programming model is constructed by incorporating multiple volatile energy prices interrelated with each other. Oil price is modelled by the mean-reverting Ornstein-Uhlenbeck process and serves as the exogenous variable in the ARIMAX models for natural gas and downstream plastic prices. The K-means clustering method is employed to extract a handful of distinctive patterns from a large number of simulated price projections to enhance the computing efficiency without losing retaining critical information and insights from the price co-movement. The model results suggest that the high volatility of the energy market weakens the possibility of selecting the corresponding technology. The oil-based route, for example, gradually loses its market share to the coal approach, attributed to a higher volatile oil market. The proposed method is applicable to other problems of the same kind with high-dimensional stochastic variables.The online version contains supplementary material available at 10.1007/s10479-021-04229-3.