Cost-of-capital valuation with risky assets

Battle Count: 94

The paper is primarily focused on insurance solvency regulation and actuarial valuation rather than quantitative trading. However, it touches on portfolio allocation between risky and risk-free assets, risk measures (VaR, ES), and the trade-off between expected return and capital requirements, which have tangential relevance to risk management in trading contexts. The limited liability option analysis and heavy-tail effects could inform risk management strategies. The paper does not address trading strategies, market microstructure, or algorithmic execution.

The Gaussian model results are fully analytical with closed-form expressions (Propositions 3.1-3.4), making them straightforward to implement. The lognormal and Pareto models require Monte Carlo simulation (1 million samples), which is computationally moderate. The theoretical framework requires understanding of risk measures (VaR, ES), stochastic orders (first-order stochastic dominance, increasing convex order), and cost-of-capital valuation. The main complexity lies in correctly implementing the solvency constraint ρ(R0Z1 - X1) = 0 and the limited liability payoff structure. No specialized software or hardware is required.

The paper provides explicit analytical formulas for the Gaussian model (Propositions 3.1-3.4), detailed parameter choices for all numerical illustrations (µ=1.05, σ=0.2, γ=1, ν=0.3, α=0.005, η=0.06), and specifies Monte Carlo simulation parameters (1,000,000 samples). All proofs are included in the appendix. However, no code or data repository is provided. The lognormal and Pareto results rely on Monte Carlo simulation without published code.