Forschungsgruppe ORCOS
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Multi-Stage Modelling of Market Disruptions

FWF Project No. P21410-G16, (03.2009 − 02.2012), Project leader: G. Feichtinger

Keywords: multi-stage optimal control, stochastic multi-stage models, illicit drugs, age-specific initiation, market disruption, Pontryaagin´s maximum principle

 

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 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.