Guaranteeing fresh and reliable information for augmented reality (AR) services is a key challenge to enable a real-time experience and sustain a high quality of physical experience (QoPE) for the users. In this paper, a terahertz (THz) cellular network is used to exchange rate-hungry AR content. For this network, guaranteeing an instantaneous low peak age of information (PAoI) is necessary to overcome the uncertainty stemming from the THz channel. In particular, a novel economic concept, namely, the risk of ruin is proposed to examine the probability of occurrence of rare, but extremely high PAoI that can jeopardize the operation of the AR service. To assess the severity of these hazards, the cumulative distribution function (CDF) of the PAoI is derived for two different scheduling policies. This CDF is then used to find the probability of maximum severity of ruin PAoI. Furthermore, to provide long term insights about the AR content's age, the average PAoI of the overall system is also derived. Simulation results show that an increase in the number of users will positively impact the PAoI in both the expected and worst-case scenarios. Meanwhile, an increase in the bandwidth reduces the average PAoI but leads to a decline in the severity of ruin performance. The results also show that a system with preemptive last come first served (LCFS) queues of limited size buffers have a better ruin performance (12% increase in the probability of guaranteeing a less severe PAoI while increasing the number of users), whereas first come first served (FCFS) queues of limited buffers lead to a better average PAoI performance (45% lower PAoI as we increase the bandwidth).