Portfolio Continuous Time CVaR Risk Measure Based On The Selection

It’s well known that Markowitz’s mean-variance portfolio theory initiated the study of mathematical methods to the financial problems of its kind, which has made a series of far-reaching results about the theory and practical applications. For decades, countless scholars have devoted to the theoretical research of this mean-variance model, which has enriched and developed the Markowitz’s portfolio selection theory greatly.In recent years, S.Emmer considered continuous-time mean-CaR-based portfolio selection problem and obtained meaningful results, such as the efficient frontier and other analytical solutions. However, this paper only considered one situation when the asset price process follows a geometric Brownian motion and the loss of wealth evaluated by CaR is based on the risk-free assets. This paper intends to work on the basis of S.Emmer’s studies, that is the study of continuous time mean-CVaR-based portfolio selection problem, which continue to carry out more profound exploration.we pay our attention on the loss based on both risk and risk-free assets when the price process satisfies a jump-diffusion stochastic differential equation.Firstly,I discuss the risk asset prices satisfying the diffusion model and jump diffusion model respectively, construct the continuous-time CVaR expression innovatively by using the Ito integral; On this basis, considering the stock price follows jump-diffusion process, I take advantage of the matlab software to solve the best investment strategy and the corresponding effective frontier of the mean-CVaR model with numerical solution. Through the comparison with the mean-variance model, show its rationality and superiority.Secondly, I analyze the continuous time utility-CVaR portfolio selection problem further. Combined with dynamic programming method and Lagrange multiplier method, the optimal investment strategy and the analytical solution of the efficient frontier are obtained clearly.