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Abstract Problem A in 2019 Mathematical Contest in Modeling (MCM) was considered. First, the dragon's growth problem was formulated into a stochastic control problem in which the food energy per unit area in its territory was the state process, and the dragon was assumed to maximize its expectation of weight by choosing reasonable control strategies (the area of the territory; the consumption rate of food; the proportion of energy intake used to defend the territory). And then the stochastic control problem was transformed into its associated Hamilton-Jacobi-Bellman equation, and the optimal strategies could be obtained via the numerical methods for partial differential equations. Finally, the weight process was given by the numerical simulation, and the sensitivity analysis of this growth model with respect to relevant environmental parameters was also considered.
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2020, Vol. 33 
