Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market
研究了跳扩散风险金融市场中大型分散投资组合的渐近动态，推导出由布朗运动和泊松过程共同驱动的简化动态，并证明当资产数量足够大时，可据此为投资组合衍生品定价和计算风险价值。
This paper studies the modelling of large diversified portfolios in a financial market with jump-diffusion risks. The portfolios considered include three categories: equal money-weighted portfolios, risk-minimizing portfolios and market indices. Reduced-form dynamics driven jointly by one Brownian motion and one Poisson process are derived for the asymptotics of such portfolios. We prove that derivatives written on a portfolio can be priced by treating the asymptotic dynamics as the underlying process if the number of assets in the portfolio is sufficiently large. Analytical and Monte Carlo value-at-risk can be computed for the portfolios based on their asymptotic dynamics.