Based on optimal control theory, we propose a model to determine the optimal allocation of resources between investment in production and prevention/mitigation measures, with the aim of maximising the expected benefit in a mountain destination facing a crisis scenario. Specifically, we consider the case of a potential crisis caused by melting permafrost, leading to a landslide and the evacuation of tourists trapped in the resort. This problem can be formulated as a Markov decision problem (MDP). In this MDP, the decision maker has to choose the optimal action at each stage of the problem in order to maximise the expected benefit in the long run, taking into account the potential risks and losses associated with a crisis scenario. The transition probabilities between states depend on the current level of investment and risk, as well as the stochastic nature of permafrost melt and landslide risk. The expected rewards associated with each action depend on the current state and potential outcomes of the crisis scenario. The actions available at each stage of the problem include investment in production, investment in prevention/mitigation measures, or inaction. By solving this MDP, through a corresponding mathematical programming problem, we can determine the optimal investment strategy that maximises the expected benefit while minimising the risk in the face of a potential crisis caused by melting permafrost and the consequences for the mountain destination. A numerical experiment based on fictitious data is proposed to show how the method can be applied.