A mean field Jacobi process for modeling sustainable tourism

Abstract

A mean field Jacobi process governing the dynamics of the travel demand of agents is formulated and its application to sustainable tourism is investigated both mathematically and computationally. The bounded nature of the Jacobi diffusion process enables the categorization of tourism state with sustainable tourism state corresponding to an internal solution and overtourism state to a boundary solution. A stochastic control framework is introduced to design sustainable tourism under uncertainty, incorporating model distortion conditions owing to misspecification. The control problem is reduced to solving the optimality system of a stationary mean field game whose closed-form solution is derived under certain conditions. The optimality system can be computed numerically using the finite difference method under more general conditions. We present demonstrative examples of the mean field Jacobi process for different parameter values, illustrating both sustainable tourism and overtourism cases. Our findings suggest that the sustainable tourism state cannot be realized if the fluctuation or model misspecification is large.