Optimal Control of Urban Health Index Including Risk Transfer and Its Analysis with Fast Monte Carlo Method

Abstract

An optimal control of an urban health index quantifying an integrity of urban performance is theoretically investigated by the use of the stochastic control theory, where three factors – recovery of the index, prevention of disasters and alternative risk transfer – are controlled. First, a probabilistic model is constructed for describing temporal variation of the urban health index with random occurrence of disasters. Next, based upon a budget structure depending on the current state of the index, optimal strategy is mathematically formulated by introducing costs associated with a recovery process, loss due to disasters and transferring risk. The HJB equation to give an optimum solution is then derived. Finally, the optimal strategy is numerically derived from the HJB equation, where a probability measure transformation technique is applied to accelerate a Monte Carlo method for estimating the cost required for the risk transfer. The results indicate that (i) optimal valance among three kinds of cost – recovery delay cost, disaster occurrence cost and a cost caused by degradation of the health index – can be realized and (ii) the importance sampling technique can improve accuracy in deriving the optimal solution.