Optimal Surplus Management for Insurers under Stochastic Interest Rates and Jump-Driven Liabilities

Battle Count: 70

The paper is primarily focused on insurance surplus management and ALM rather than direct quantitative trading. However, the stochastic control framework, CIR interest-rate modeling, exponential utility optimization, and myopic-hedging decomposition are directly relevant to portfolio optimization and risk management in quantitative finance. The investment strategy decomposition (myopic + intertemporal hedging) parallels techniques used in multi-asset portfolio management. The numerical PDE approach is transferable to derivative pricing and optimal execution problems.

Implementation requires: (1) solving a coupled nonlinear PDE system via implicit finite differences with fixed-point iteration, (2) handling CIR boundary conditions (degenerate at r=0, zero-gradient at r_max), (3) enforcing the admissibility constraint A < ξ, (4) computing matrix inverses for the covariance structure, (5) Monte Carlo simulation for validation. The mathematical derivation is complex (HJB, exponential ansatz, projection method), and numerical stability near the jump-term singularity requires careful handling. Expertise in stochastic control, numerical PDEs, and actuarial mathematics is needed.

The paper provides detailed parameter tables, explicit PDE system, numerical scheme description (finite differences, fixed-point iteration, boundary conditions), and grid convergence tests. However, no code or repository is provided. The methodology is fully described mathematically, enabling reproduction by an expert in stochastic control and numerical PDEs. The illustrative (non-calibrated) nature of numerical experiments limits direct empirical reproducibility.