Capturing cash non-additivity and horizon risk via BSDEs and generalized shortfall

Battle Count: 94

The paper provides theoretical foundations for risk measures that account for horizon risk and interest rate uncertainty, which are relevant for multi-horizon portfolio management and risk assessment. However, it is purely theoretical with no direct trading strategies, numerical methods, or empirical results. The BSDE framework and dynamic risk measures have indirect relevance to quantitative risk management in trading contexts, particularly for long-horizon positions and pension fund management.

Extremely high complexity requiring deep expertise in stochastic analysis, BSDE theory (both Lipschitz and quadratic), convex analysis, risk measure theory, and Tsallis entropy. The mathematical machinery involves Girsanov theorem, comparison theorems for BSDEs, acceptance set representations, and dual representations of quasi-convex risk measures. No computational implementation is provided.

This is a purely theoretical mathematical paper with no code, numerical experiments, or empirical validation. Reproducibility depends on the reader's ability to verify the mathematical proofs and derivations. No computational implementation is provided.