Multi-Stage Modelling of Market Disruptions

In many decision situations arising in economics and Operations Research it is assumed that the underlying systems (markets) evolve continuously. However, in the real world there are often discrete shocks to the system that are, for example, triggered by sudden political or institutional changes. Such a shock can fundamentally change the system dynamics at particular points in time. The decision maker`s challenge is to find the new optimal strategy. The rapidly developing field of multi-stage optimal control models (MSM) addresses such difficult situations and aims at dealing with them optimally. This project adapts and further develops MSM methodology and thereby contributes to the propagation of a new powerful tool for dynamic optimization. Using the MSM methodology we want to discuss important questions pertaining to the control of illicit drug use. (1) How should drug policy react to uncertainties, such as market disruptions of unknown length as the recent supply and price shock in the Australian heroin market? (2) Many, if not most countries have to cope with drug problems of more than one substance of abuse. What is the impact of a price shock in an interacting drug market that only affects one substance? (3) How can sudden behavioural changes in a drug market be used when initiation is age-specific? We analyze these three questions by utilizing optimal control theory. Optimal control models are limited in complexity, so we enrich our analyses by developing an empirically validated system dynamics model of heroin use in Europe. This complex and hence more realistic model is interesting in its own right and furthermore allows us to test the results of the optimal control models. Over the course of this project we expect not only to find answers to these relevant questions of drug policy, but also to advance the mathematics of MSM and use this framework for other applications. Inherent nonlinearities which arise from social interactions in the drug initiation and drug markets generate multiple equilibria, history dependence, and sensitivity to initial conditions. These problem characteristics make drug policy a particularly interesting case study for MSM methods, and the structure of the associated policy problems will lead to interesting extensions of these methods.

In many decision situations arising in economics and Operations Research it is assumed that the underlying systems (markets) evolve continuously. However, in the real world there are often discrete shocks to the system that are, for example, triggered by sudden political or institutional changes. Such a shock can fundamentally change the system dynamics at particular points in time. The decision makers challenge is to find the new optimal strategy. The rapidly developing field of multi-stage optimal control models (MSM) addresses such difficult situations and aims at dealing with them optimally.This project adapted and further developed MSM methodology and thereby contributed to the propagation of a new powerful tool for dynamic optimization. Using the MSM methodology we discussed important questions pertaining to many different applications.An important topic treated within this project was related to drug consumption. We considered the impact of different exogenous shocks, such as market disruptions, and saw that such shocks can eventually have tremendous irreversible positive as well as negative consequences. We found that the success of a sudden change in drug policy is tremendously influenced by heterogeneities among drug consumers and analyzed the impacts which can arise by the anticipation of such a shock.Related to recent events, we considered the impact of market disruption of capital markets due to a recession of unknown duration on producers of conspicuous consumption goods, i.e. goods where demand increases with the price. We gained important insights concerning the optimal pricing strategy as well as the optimal handling of cash reserves.Over the course of this project we not only found answers to relevant questions in various applications, but also advanced the mathematics of MSM. We considered inherent nonlinearities generate multiple equilibria, history dependence, and sensitivity to initial conditions. We found, amongst other things, that so-called Skiba points, i.e. points at which a decision maker is indifferent between two different long-run solutions, crucially depend on the switching times between two stages, that indifference can arise (as well as disappear) through the inclusion and the increase of switching costs, and that through the consideration of several stages additional candidates for the optimal solution must not be neglected.