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Emanuel RAPSCH (TU Berlin) “On Controlled Stopping Games and Transition Risk”

December 13, 2021 @ 3:30 pm - 4:30 pm
GT “Modèles stochastiques en Finance”
Time: 15:30 p.m. to 16:30 p.m.
Date: 13th of December 2021
Room : 3105

Emanuel RAPSCH (TU Berlin) “On Controlled Stopping Games and Transition Risk”

Abstract :: We study the Nash system of a (non-necessarily homogeneous) $n$-player game of optimal stopping in the presence of common strongly Markovian noise. For linear diffusions, we derive a one-to-one characterisation of subgame-perfect feedback Nash equilibria in terms of this coupled free-boundary type system of differential equations, whence a method of constructing these equilibria and devising conditions on both their existence and number. If the game’s rules can be controlled by a principal through a decision at its beginning, the decision problem of choosing between different regimes of equilibria can be mathematically addressed.

A major motivation for this work stems from the challenge of technological transitions in second-best, strategic market interactions under a commonly faced uncertainty. In sectors like the automotive or steel industry, high-fixed cost make investment irreversible, yet uncertainty about consumer preferences or infrastructure deployment is of the essence. Our model offers a means of analysing this timing decision in heterogeneous, concentrated market situations and providing guidance for firm valuation. Moreover, it could, based on macroeconomic scenarios and corresponding cost estimates, give answers to the public policy problem of implementing large-scale (e.g. climate) targets on the smaller scale of a specific sector. Conversely, it could provide a sector-specific backtesting method for these scenarios using implied quantities.
In the upcoming talk, I would like to focus on the first paragraph, give an outlook on the second, and therefore discuss the links between stochastic analysis, finance, and risk analysis in the context of climate change and biodiversity. This is ongoing doctoral research supervised by Christoph Belak.