Entropic Vaiue-at-Risk And Optimal Portfolio Selection

Since the modern portfolio theory was created by Markowitz in1952, portfolio selection has been a hot research theorists. The core of the portfolio selection is to select the appropriate risk measurement meth-ods and effective asset allocation. So far, experts and scholars have been proposed, such as Variance, VaR, CVaR, CAR, CCAR and so many different risk measurement methods, and the corresponding as-set allocation model, which has accumulated a wealth of results for the theoretical and practical circles.Ahmadi-Javid, used Chernoff inequality in the calculation of VaR in2012, proposed a new class of Coherent risk measurements:the en-tropy value-at-risk (EVAR) and g-entropy risk measure.At the same time,they gave these risk measurements’ representation theorems. EVaR is proved to be an upper bound of CVaR,which is more risk-averse and efficient in dealing with some stochastic optimization problems than CVaR. In this paper, we extend the results of Ahmadi-Javid,to study the dynamic situation. We give the definitions of conditional EVaR and conditional g-entropy risk measure, and their representation theorems. Finally, we study EVaR optimal portfolio selection in continuous-time and discrete-time, respectively. We solve the optimal portfolio used analysis and numerical methods, and give a empirical analysis compared to CVaR optimal portfolio selection.