Research On The Optimal Investment Problem Of Enterprise Annuity Containing Default Bonds

Along with our country the aging of the population structure,the optimal investment problem of enterprise annuity has become an important research topic in the field of endowment insurance in our country at present.The enterprise annuity is refers to the enterprise and its worker on the basis of attend primary endowment insurance lawfully,volunteered to set up a system of compensatory endowment insurance.The basic treatment of enterprise annuity plan is divided into fixed type Defined Benefit type(hereinafter referred to as DB type)and Defined Contribution type(hereinafter referred to as DC type)two modes.In the DB type enterprise annuity plan,financial market and the investment risk of enterprise annuity participants longevity risk borne by the fund company completely,and in DC type enterprise annuity plan,Investment risk and longevity of the participants is the shift from fund managers to enterprise annuity individual participants,leading to more researchers are keen to DC type exploration of the enterprise annuity plan and get the optimal investment strategy also is particularly important in the financial markets.This paper mainly studied the contains default risk DC type enterprise annuity,the optimal investment problem,and get the following three aspects of conclusions.First,assumes that the enterprise investor to enterprise annuity investment in the risk-free asset(bank),risk assets(shares)and the three parts can be defaulted bonds.Due to the particularity of the enterprise annuity inflows and outflows,since it contains both model in the enterprise each stage financing investment returns,joined the inflow of each individual pay pay cost.The staff issue payment in accordance with the employee wages by fixed ratio calculation.This model to maximize the wealth as the goal,using the dynamic programming principle to get HamiltonJacobi-Bellman equation(HJB equation is used as the abbreviation below)about the optimal investment strategy;In the case of exponential utility function,the explicit solution of the optimal strategy is obtained by stochastic control method.Finally,some parameters in the results are analyzed numerically.Second,study dc type enterprise annuity investment in risky assets,bank deposit or contain any debt default risk when the three types of assets the optimal investment proportion of the biggest benefits of wealth.The difference is that will be in front of the fixed rate into a stochastic interest rate.Because in the actual capital market,interest rate is changed over time,so the stochastic interest rate will be more in line with the actual investment environment.Through the establishment of HJB equation to solve the optimal investment strategy,and given some the value of the parameter,numerical analysis was carried out on the investment strategy of time curve.Finally,for the first two parts of the model was improved,the enterprise annuity investment is no longer a kind of can be defaulted bonds but to invest in multiple default combination of debt and the bonds between default contagion,namely the default occurs between a single bond is can infect each other.Assuming that corporate investors put money to invest in risky assets,bank deposits,government bonds and multiple can be defaulted bonds,establish dynamic programming equation,using martingale method respectively to solve the general utility function and the optimal investment strategy under exponential utility function,and numerical simulation analysis of bonds investment strategy.