A financial market with interacting investors: does an equilibrium exist?

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A class of globally solvable Markovian quadratic BSDE systems and applications (2016, background): “A simple nonexistence example given in [33] illustrates this point quite effectively.”
7 – Backward Stochastic Differential Equations (2011, unknown): “Moreover, Frei and Dos Reis [35] found a multidimensional quadratic BSDE with a bounded terminal condition which does not have a solution.”
OPTIMAL INVESTMENT UNDER RELATIVE PERFORMANCE CONCERNS (2015, background): “In particular, [12] highlights the difficulty in the existence and uniqueness of the quadratic multidimensional backward SDE of the present paper, and established the existence of a sequentially delayed Nash equilibrium in the general case.”
Mean field and n‐agent games for optimal investment under relative performance criteria (2017, background): “…when (𝜇𝑖, 𝜎𝑖) = (𝜇, 𝜎), and 𝜈𝑖 = 0, for 𝑖 = 1,… , 𝑛, for some 𝜇, 𝜎 > 0 independent of 𝑖. Notably, the single stock case was studied in Espinosa and Touzi (2015) and Frei and Dos Reis (2011) in greater generality, incorporating portfolio constraints and more general stock price…”
Multidimensional quadratic and subquadratic BSDEs with special structure (2013, background): “In fact, multidimensional BSDEs with drivers of quadratic growth in z do not always admit solutions even if the terminal condition j is bounded; see [9] for an example.”