Maximum principle for robust utility optimization via Tsallis relative entropy

Battle Count: 259

The paper provides a rigorous theoretical foundation for robust portfolio optimization under model uncertainty using Tsallis relative entropy. While directly relevant to quantitative trading strategy design (optimal consumption-investment under ambiguity), it is purely theoretical with no empirical validation or numerical implementation. The maximum principle and forward-backward system could inform algorithmic trading strategy development, but significant work would be needed to translate these results into practical trading algorithms. The Tsallis entropy framework offers a more flexible model of ambiguity aversion than classical relative entropy.

Extremely high complexity. The paper involves advanced stochastic analysis including quadratic BSDEs with f(y)|z|^2 generators, Itô's formula transformations, stochastic flow methods, convex analysis in infinite-dimensional spaces, and coupled forward-backward systems. Implementing the theoretical results would require solving nonlinear BSDEs numerically, handling the Tsallis entropy distortion, and solving the coupled FBSDE system. No code or numerical algorithms are provided.

This is a purely theoretical mathematics paper with no computational experiments, code, or numerical results. Reproducibility is limited to verifying the mathematical proofs. All results are analytical theorems and propositions with complete proofs provided in the paper and appendices.