Risk-averse stochastic path detection

We introduce the stochastic path detection problem and propose a risk-averse solution approach. The problem comprises an invader and a protector that both operate on a network with a number of possible source-destination paths. The protector aims at allocating security resources on the network such that the invader's path is detected with high probability. The invader's choice of path is known to the protector in terms of a probability distribution reflecting the protector's beliefs. Errors in these beliefs induce the risk of a low detection probability. We derive a linear programming approximation and leverage the theory of coherent risk measures to consider risk-aversion with respect to errors in the protector's beliefs. The performance of the resulting risk-averse detection policy is numerically compared with the performance of the risk-neutral policy. We show that the risk-averse policy significantly mitigates the risk of facing a low detection probability in the presence of large errors in the protector's beliefs.