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BIRS Workshop Lecture Videos

Finding local equilbria by splitting multidimensional BSDEs Frei, Christoph


We consider a model of a financial market where investors take not only their own absolute performance, but also the relative performance compared to their peers into account. The goal is to find equilibria where every investor has an individually optimal strategy. This problem is related to the study of multidimensional backward stochastic differential equations (BSDEs). We introduce a new notion of local solution by splitting multidimensional BSDEs over time. This allows us to show that the BSDE from our financial problem is locally but not globally solvable. From this, we deduce that there exist local but no global equilibria in our model of a financial market. By considering the relative performance, investors may ruin each other so that equilibria exist only over a short time.

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