Research On Quantile Capital Allocation

With the continuous changes in the financial market,financial risk management plays a role that cannot be ignored in application fields such as capital allocation and investment portfolios.In the application process,it is often necessary to calculate or estimate the expected value of a random variable to measure the risk,usually using the quantile Euler capital allocation method,also known as the Value at Risk(VaR)method,it is to use the quantile of the random variable at a pre-specified probability level as the value of its risk measure,but the convergence rate of the classical nonparametric estimation of this method is lower than the standard rate and does not satisfy the subadditivity.Since capital allocators have different risk preferences,we use MCVaR with an optimistic coefficient to measure risk,establish its relationship with expected shortfall(ES),and prove that MCVaR satisfies the subadditivity.Under the premise of assuming a fixed optimism coefficient,by adjusting the relevant probability levels to make the MCVaR equal to the VaR at the original probability level,and then obtain the nonparametric estimation based on the MCVaR risk metric allocation under the new probability level,and draw the conclusion that the allocation method converges at the standard rate through the proof.Finally,we derive the asymptotic distribution form of the nonparametric estimator assigned by MCVaR based on the data in the mixed setting,in order to evaluate the performance of this nonparametric estimator,we further propose an AR-GARCH model to fit each risk variable,and employ a residual-based bootstrapping method to quantify the uncertainty of the estimation,observe the performance of a limited sample is observed through simulation studies.