An Optimal Stopping Approach to Portfolio Risk Measurement

Description

Portfolio risk measurement under nested setting has received increasing attention among simulation researchers and practitioners in recent years. Under nested setting, simulation is required to re-evaluate the portfolio value at a future date, making the problem extremely computationally challenging. Portfolio risk measurement under such setting often involves a two-level simulation procedure, in which one first simulates a number of possible scenarios of risk factors up to a future time horizon in the outer level, and then in the inner level evaluates the mark-to-market loss of the portfolio for each outer-level scenario.In this project, we propose an optimal stopping approach in which only one observation is required in the inner-level simulation for each outer-level scenario, thus reducing the computational burden arising from the two-level simulation procedure. In particular, we show that conditional value-at-risk (CVaR) of the portfolio can be represented as the optimal value of a stochastic program which involves an appropriately constructed optimal stopping problem. Then various methods in the literature of optimal stopping can be borrowed to estimate CVaR. As a by-product, the approach also leads to an estimate of value-at-risk (VaR).We expect that the optimal stopping approach will serve as a viable tool for portfolio risk measurement problems in practice. In addition to estimation of VaR and CVaR, we plan to investigate its use in portfolio optimization, including mean-CVaR optimization under nested setting, and multistage risk adverse portfolio optimization. It is expected that outputs of this project will provide useful simulation techniques to portfolio optimization.