Loan Portfolio Optimization Model Under Uncertain Distribution

The core risk of loan portfolio is credit risk,which stems from the possibility of default by the lender of the loan.The loan portfolio optimization method is an important means of credit risk management.Using portfolio optimization approach to rationally allocate capital can help investors balance safety and profitability,ensure that investment returns are maximized within acceptable risk limits,or minimize risks within acceptable expected returns.There are two difficulties in the application process of loan portfolio optimization:Firstly,the historical data of loans is lacking or even unavailable.How to accurately measure credit risk and operate portfolio optimization under the condition of historical data unavailable?Secondly.the loss distribution of loans is uncertain.How to incorporate the uncertainty of loss distribution into the investment decision-making process and improve loan portfolio optimization?This paper focuses on the two difficulties of "lack of historical data" and "uncertainty of loss distribution" in the loan portfolio optimization problem.We study the credit risk measurement.as well portfolio optimization,under the condition of historical data unavailable and loss distribution uncertainty for bank loans and P2P loans respectively.The main research contents of this paper are as follows:(1)For the lack of bank loans' historical data,a bank loan portfolio optimization model based on non-parametric kernel estimation is proposed.Firstly,by constructing the discrete function relationship of bank loan loss to macroeconomic conditions and loan health status,bank loan loss is estimated under Monte Carlo simulation,which can improve the bank's capability of loan portfolio risk management.Secondly,by using the non-parametric kernel estimation method to estimate the portfolio loss distribution,and using the conditional value at risk(CVaR)model of the loan portfolio,we construct the bank loan portfolio optimization model,which improves the accuracy of loss distribution estimation,enhances the risk control ability of investors and reduces the possibility of catastrophic portfolio loss.(2)For the uncertainty of bank loan loss distribution,a bank loan portfolio optimization model based on mixed distribution is proposed.Firstly,a set of bank loan portfolio loss distributions is constructed by using Monte Carlo simulation of macroeconomic conditions and portfolio loss distribution estimation based on central limit theorem(CLT),which solves the problem of potential distribution estimation and selection in portfolio optimization under distributed uncertainty.Secondly,by constructing the CVaR model under mixed distribution,the possible loss distributions under various macroeconomic conditions is incorporated into the investment decision-making process,which improves portfolio optimization model and reduces the potential risk of the final portfolio.(3)For the uncertainty of P2P loan loss distribution.a robust optimization model of P2P loan portfolio based on data-driven and relative entropy constraints is proposed.Firstly.the kernel regression method is used to estimate the expected return and risk of P2P loans,and the set of uncertain distributions is established according to the relative entropy constraints,and then the robust optimization model of P2P loan portfolio is formulated,which improves the efficiency of the P2P loan portfolio and obtains high investment return.Secondly.a data-driven cross validation method is used to optimize the level of distribution uncertainty.which can avoid the bias caused by the subjective setting.and ensure that rational investment return could be obtained even if the difference between the estimated value of the parameters and the actual value is relatively large.According to the results of numerical experiments.this paper finds that:1)The bank loan portfolio optimization model based on non-parametric kernel estimation proposed in this paper has stronger risk control ability than the classic portfolio optimization model based on empirical distribution which can balance the return and risk of loan portfolio better and achieve higher returns under unit risk.2)Taking the loss distribution uncertainty into the loan portfolio optimization process,financial institutions can effectively reduce the portfolio risk and improve the investment efficiency.As for the bank loan portfolio optimization problem,the average CVaR model under the mixed distribution condition proposed in this paper is better than the worst-case CVaR model in the existing study from the perspective of risk mitigation.3)The loan evaluation model based on median kernel regression can accurately estimate P2P loans' expected return and risk and achieve higher prediction accuracy compared with the classical mean kernel regression model.Further.based on the median kernel regression,the P2P loan portfolio optimization model can obtain higher investment returm than existing model.4)For P2P loan investment,taking the loss distribution uncertainty into the risk measurement and portfolio optimization process can reduce the risk generated by the parameter estimation bias,and improve the investment performance.Further.the level of the distribution uncertainty is an important parameter to ensure the effectiveness of the portfolio optimization,which can be optimized by the method of data-driven cross-validation.