Risk diversification for infinitely divisible distributions

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Highly relevant for risk management and portfolio construction strategies involving heavy-tailed assets. It challenges the conventional wisdom of diversification for certain infinite-mean risks, which is critical for tail-risk hedging and capital allocation in quantitative finance.

Implementing the theoretical results requires advanced knowledge of stochastic calculus, Lévy process theory, and measure theory. Direct application to trading algorithms would require significant adaptation from theoretical conditions to practical risk metrics.

The paper is purely theoretical with complete mathematical proofs provided in the appendix. All definitions, theorems, and derivations are self-contained and rigorous, allowing for full verification by experts in probability theory.