Competitive optimal portfolio selection under mean-variance criterion

Battle Count: 164

The paper provides a rigorous theoretical framework for competitive portfolio selection under mean-variance preferences in non-Markovian markets. While highly relevant to institutional investors competing for relative performance, the results are primarily analytical and do not provide directly implementable trading algorithms. The Nash equilibrium characterization via BSDEs could inform competitive fund management strategies. The three-scenario classification (unique/none/infinite equilibria) has practical implications for market design and competitive dynamics among fund managers.

Extremely high complexity. The paper involves coupled systems of SDEs and BSDEs, non-homogeneous stochastic LQ control, decoupling techniques, fixed-point arguments for novel BSDE classes, and multi-dimensional linear algebra (Moore-Penrose pseudoinverse). Implementing the feedback strategies requires solving the coupled BSDE system (4.6) numerically, which involves computing the fundamental solution matrix Γ, the matrix K, and determining invertibility of (I_n - K). The non-standard BSDE with driver depending on h(0) poses significant numerical challenges.

The paper is purely theoretical with complete mathematical proofs. All derivations, lemmas, and theorems are self-contained. However, there are no numerical experiments or code implementations provided. Reproduction requires advanced knowledge of stochastic calculus, BSDE theory, and LQ control. The evaluation table (Table 1) summarizes main results clearly.