Optimal portfolios with stress analysis and the effect of a CVaR constraint

Risk-constrained allocation of risky assets in financial portfolios is particularly important in situations when asset returns appear to have large fluctuations. This problem is addressed here. The asset price is assumed to be driven by a Brownian motion perturbed by a compound Poisson process. This resembles a price process perturbed by an exogenous factor which may cause large movements in price. The jump size of the Poisson process and the rate of jump define, respectively, a scenario and its occurrence probability. The stress testing is conducted to evaluate the performance and assess the resilience of the portfolio subject to exceptional but major events. We examine how a conditional-value-at-risk constraint exerts an influence on the portfolio composition.