Behavioral Participating Insurance: Optimal Investment under Probability Distortion and Aspiration Constraints

Battle Count: 75

The paper is primarily focused on insurance asset management rather than direct quantitative trading. However, the portfolio optimization framework, probability distortion effects on investment strategies, time inconsistency analysis, and regime-switch behavior in optimal policies are relevant to behavioral portfolio management and institutional asset allocation. The explicit closed-form solutions under distortion could inform trading strategies that account for behavioral biases. The Black-Scholes setting and martingale duality methods are foundational to quantitative finance, but the insurance-specific payoff structures (participating contracts, guarantees, surplus sharing) limit direct applicability to typical trading contexts.

The paper involves highly complex mathematical machinery: quantile formulation, concave-envelope relaxation, martingale duality in incomplete markets, PHARA utility characterization with multiple piecewise segments, inverse S-shaped probability distortion, aspiration constraints, and labor-capital adjustment. The closed-form solutions involve numerous conditional expectations, generalized inverse functions, and case-by-case analysis depending on initial wealth levels and Lagrange multiplier positions. Numerical implementation would require careful handling of the piecewise structure, the distortion function composition with Gaussian kernels, and the aspiration constraint feasibility checks. The formulas span multiple pages with intricate notation.

The paper provides fully explicit closed-form formulas for optimal terminal wealth and portfolio processes, along with specific numerical parameter settings for all figures (µ=0.07, r=0.01, σ=0.15, T=1, a=1.17, b=0.86, z̄=0.33, Lg_T=1, p=0.4, η=0.6, x0=1). However, no code repository or supplementary computational scripts are provided. The mathematical derivations are self-contained with proofs in appendices, enabling theoretical reproduction but requiring significant effort for numerical implementation.