Meyer Risk Measures

Battle Count: 60

Highly relevant for risk management and portfolio selection in quantitative trading. The paper provides a flexible framework for capital requirement computation that interpolates between Loss VaR and adjusted ES, with explicit control over risk aversion. The λ-SD-consistent risk measures can better capture heavy-tailed behavior than adjusted ES, which is critical for tail risk management. The benchmark-relative risk measures (Section 3.3) are directly applicable to active portfolio management. The systemic risk framework (Section 3.5) is relevant for institutional risk monitoring. However, the paper is primarily theoretical and does not provide trading strategies, signal generation, or execution algorithms. The practical computation is straightforward (comparable to classical ES), making implementation feasible.

The theoretical framework is mathematically sophisticated (stochastic orders, representation theorems, impossibility results), but the practical computation of λ-SD-consistent risk measures is explicitly stated as 'not more complex than computing a classical ES' (Section 3.2). The key formulas involve: (1) computing ρ_{λ,p}(X) = -e^{-1/λ}∘(-ES_p)∘e_λ(X), which requires computing ES of exponential-transformed payoffs; (2) taking suprema over p∈[0,1] with target risk profiles g(p); (3) taking infima over families G. For step-function target profiles, this reduces to finite maxima. The Black-Scholes portfolio example and empirical log-return analysis are computationally straightforward. The main complexity lies in choosing appropriate threshold utilities and target risk profiles.

The paper provides explicit distribution parameters (Table 1), Black-Scholes market parameters, and uses publicly available stock index data (S&P 500, DAX, FTSE, DJI, NASDAQ, N225, STOXX50E) with specified time periods. Opening prices are used. However, the paper is primarily theoretical with no code repository mentioned. The mathematical proofs are self-contained in appendices. Reproducing the numerical examples requires implementing the λ-SD-consistent risk measure formulas, which are explicitly given.