The subject of this paper is modelling and optimal control of consumption and exploration of non-renewable resources via piecewise-deterministic Markov processes (PDP). In general, one asssumes that new reserves are found at random times T1, T2, T3,…, where the inter-arrival times are exponentially distributed. The amount of resource found at each Ti is also a random variable with a given distribution. This process falls into the category of PDP. In this paper, we clearly show how one can apply the PDP optimal control theory to the optimal consumption and exploration of non-renewable resources under uncertain exploration. The advantage of using a PDP model is that no matter how complicated the dynamics, utility function and distribution functions are, as long as they satisfy some mild assumptions, one can easily transform the problem into a deterministic optimal control problem, which can be solved iteratively with guaranteed convergence for the value function.
