The Application Of CVaR In Bond Investment And Re-manufacturing Optimal Production Planning

After the Conditional value-at-risk (CVaR)was raised, which is widely used in areas such as finance,water and electricity, supply chain, etc. However, the research about what applying to the bond portfolio which in the financial field and re-manufacturing production planning is rarely, the paper focus on the research of applying CVaR to the two fields mentioned above.In this paper, we mainly consider the problems of bond portfolio optimization and the re-manufacturing production planning which are based on CVaR, the main researches include the following two aspects:Firstly, for the difficulty of risk measurement in the bond portfolio prob-lem, we establish the bond portfolio optimization model based on CVaR by using CVaR as risk measure means. Due to the smoothness and randomness of the model, we introduce an auxiliary variable to deal with the non-smooth function and convert the model into the stochastic linear programming model. Then we use the Monte-Carlo simulation to discrete the problem, but it is quite difficult when samples become larger. Hence, we consider the method based on the smoothing nonlinear model. By a smoothing technique, we convert the non-smoothing bond portfolio optimization model into a smooth optimization model, which has global optimal solution. As for the simulation, we give a smoothing method and a lin-ear programming method (LP). Both two methods can solve the bond portfolio optimization problem efficiently, and numerical results prove that the smoothing method is better than the LP method, which has global convergence. Our work can provide the basis of reference and decision-making for the bond investors to do better in risks averse.Secondly, for the problem of the re-manufacturing integrated production planning problem, we establish a joint probability constrained optimization model for the re-manufacturing enterprise integrated production planing on single prod-uct in the circumstance of the uncertainty on market demands and recycled waste products. Due to the probability function in constraints is hard to obtain explicit expression, there exist many difficulties in translating and solving of the model. We consider convex approximation to convert the model at the beginning, then using the CVaR approximation method to continue to convert the model.Because of what the model we obtained whose constraints contain random variables, then we use the sample average approximation approach (SAA) to solve CVaR ap-proximation for the series of convex problems. We obtain independent identically distributed samples of random variables by Monte-Carlo simulation, then use lin-ear programming method to solve this problem and give convergence analysis for the model. Finally a specific example of re-manufacturing enterprise is given as numerical experiment,and the numerical results prove the effectiveness of the model and the algorithm.