Research On Portfolio Models With Realistic Factors In The Presence Of Background Risk And Their Applications

Traditional investment decision models assume that investors only face the investment risk.However,investors also face background risk,and the asset that are exposed to background risk as background asset.Among the existing researches,background risk has been divided into two parts,including additive and multiplicative background risk(referred to as two types of background risk).In addition,investors make investment decisions not simply by return and risk.In reality,they usually take more factors into account,such as the financial status of securities issuers,short-selling mechanism and their own bankruptcy risk.Therefore,the portfolio problem with background risk and realistic factors is close to reality and meaningful.This paper mainly studies from the following aspects:(1)We construct an investment decision model with related background risk.Against the shortcoming of researches ignoring the correlation between the two types of background assets,this paper derives a certainty equivalent with the correlation by the expected utility theory.Then,we obtain the optimal investment strategy and result by functional behavior analysis,and we analyze the impact of the correlation on them.Finally,we provide a numerical example to illustrate the idea of the model.Compared with existing researches,the investment situation with the correlation of the two types of background asset is more general,(which is referred to as related two-background-risk situation in this paper)and the next portfolio problems with realistic factors are based on this situation.(2)We construct a portfolio model with conservative short-selling and financial distress in the presence of background risk.Reducing or avoiding investment on the securities issuers that suffer in financial distress,can help investors avoid losses caused by financial distress.This paper aims at maximizing return,minimizing risk and minimizing financial distress,and constructs a portfolio model with financial distress and background risk.Then,the elitist non-dominated sorting genetic algorithm(NSGA-II)is used to solve the model.Finally,an example analysis is used to illustrate the effectiveness of the model and the algorithm,and analyze the impact of background risk on the investment.(3)We construct a portfolio model with bankruptcy control and background risk.Investors always avoid bankruptcy in investment.This paper constructs a portfolio model with bankruptcy control and background risk which maximizes the final wealth and minimizes the risk of investment.We transform the dual-target model into a single-target model by standardization and trade-off coefficient.Then,the particle swarm optimization algorithm is used to solve the model.Finally,an example analysis is used to illustrate the effectiveness of the model and the algorithm,and analyze the impact of background risk on the investment.Based on the above research,we can find that background risk pays a significant impact on investment.Investors who face background risk should take the background assets and their correlations into account.