Research On Uncertain Portfolio Selection Model With Background Risk And Loss Aversion

In recent years,with the development and gradual improvement of China’s financial market,investment activities in the market have shown a clear upward trend.Investment activities and risks are accompanied by each other.Especially with the increase of financial products and financial derivatives,investors need more professional investment knowledge and investment skills to establish a portfolio selection model to reduce risks.The classic portfolio model assumes that investors are only facing financial risks.In fact,in addition to financial risks,investors also face background risks such as labor income,health,and holdings of real estate.In addition,the classic portfolio theory assumes that investors are rational,but a large number of empirical results show that portfolio behavior could affected by individual psychology.Investors are generally loss-averse.Their utility comes from the change of wealth rather than the absolute level of wealth.The negative effect of loss is greater than the positive effect brought by the same amount of income,which means investors are more sensitive to lose than gain.The above research is mainly based on probability theory,which regards securities income as a random variable.However,the basis of applying the theory of probability stochastic is that there is enough effective historical data.In reality,there are cases of lack of historical data of assets in financial markets.Therefore,based on the uncertainty theory,the impact of background risk and loss aversion on the portfolio are considered.The main contributions of this paper are as follows:First,we present an uncertain mean-chance portfolio model with two types of background risks.Investors not only face the risk of asset price fluctuations,but also face the additive background risk brought by factors such as labor income,and the multiplicative background risk caused by factors such as inflation.This paper regards the securities return rate and the background risk return rate as uncertain variables introduces the background risk into the uncertain mean-chance model in the form of additive and multiplicative,respectively,and establishes the uncertain mean-chance based on the background risk preference.Model and uncertainty mean-chance model based on multiplicative background risk.Assuming that the securities yield and the background risk return rate obey the uncertain normal distribution,the equivalent form of the uncertain mean-chance model based on the background risk preference is given.The numerical examples illustrate the validity of the model.The results of the example show that when the tolerable chance level is the same,the greater the additive background risk preference,the higher the investor’s expected return;when the additive background risk preference is the same,Investors expect that returns will increase as the level of tolerable opportunities rises;when the tolerable chance level and the additive background risk preference are the same,investors expect the return to increase as the additive background risk increases.Second,we propose a two-objective uncertain portfolio model with background risk.Based on maximizing uncertain expectation and minimizing uncertainty variance,this paper establishes a two-objective uncertain mean-variance model considering background risk.Assuming that the securities and the background risk return rate obey uncertain normal distribution,the equivalent form of the double-objective uncertain portfolio model with background risk is suggested.In order to solve the model,an improved p-norm dominance index is constructed and proved to be equivalent to Pareto dominant.Based on the index,an improved hybrid multi-objective genetic algorithm based on p-norm is designed.Third,we study a multi-objective uncertain portfolio model that considers background risk and real-world constraints.With consideration of background risk,liquidity constraint,borrowing constraint and cardinality constraint,we establish a three-objective uncertain portfolio model.Assuming that the securities and the background risk return rate obey uncertain normal distribution,the equivalent form of the three-objective uncertain portfolio model with background risk and the realistic constraint is given.In order to solve the model,an improved hybrid multiobjective evolutionary algorithm based on elite retention strategy is designed.Fourth,we propose a portfolio model with loss aversion which is based on uncertainty theory.Given the assumption that the securities are subject to an uncertain normal distribution,the equivalent form of model is presented.The results of the example show that with the same degree of loss aversion,the expected utility of the investor increases if the level of tolerable chance increases.When the level of tolerable chance is the same,the greater the loss aversion,the less the investor’s expected utility.As the value of the reference point increases,investors expect the utility to gradually decrease.In addition,the liquidity constraint is introduced into the uncertain portfolio with loss aversion,and the impact on the introduction of liquidity is compared.The uncertainty of the liquidity constraint is considered to be less than the liquidity constraint when other parameters are unchanged.Finally,an uncertain portfolio selection model is proposed considering both background risk and loss aversion.As investors face both background risks and general aversion and aversion tendencies,they consider both background risk and loss aversion,and propose an uncertain mean-chance model that considers background risk and loss aversion.Investigate the marginal and joint effects of background risk and loss aversion on uncertain portfolios.The results are as following: Given income level and tolerable chance level,the expected utility of the optimal portfolio with loss aversion is less than the optimal value without loss aversion.The expected utility of the optimal portfolio with background risk and loss aversion is less than the background risk.The above conclusions were verified by numerical examples.