Optimal Allocations with Distortion Risk Measures and Mixed Risk Attitudes

Battle Count: 79

The paper is primarily relevant to risk management and insurance rather than direct trading strategies. However, the characterization of optimal risk-sharing between risk-averse and risk-seeking agents has implications for understanding market microstructure, hedging strategies, and portfolio construction in markets with heterogeneous participants. The counter-monotonic (betting) allocations among risk-seekers could inform understanding of speculative trading dynamics. The inf-convolution framework is relevant for optimal hedging and risk transfer in quantitative finance.

The theoretical framework requires advanced knowledge of convex analysis, measure theory, and mathematical finance. Implementing the inf-convolution computations for specific distortion functions (especially piecewise-linear ones) is tractable, but the general problem involves solving constrained optimization over function spaces. The reduction from n-agent to 2-agent problems simplifies computation, but explicit solutions are only available under restrictive assumptions. Numerical implementation would require careful handling of the non-convexity arising from mixed risk attitudes.

The paper is purely theoretical with complete mathematical proofs provided. All results are derived analytically from stated assumptions. No empirical data or code is required for verification. The mathematical framework is self-contained with clear definitions and theorem statements. However, the complexity of the proofs (especially in Sections 4-6) requires significant mathematical maturity to verify independently.