In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows ...In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.展开更多
According to the data from IFSL(International Financial Services, London), Pension funds increased rapidly in recent year. Pension funds always have different ways to build up. One form always from the institutional i...According to the data from IFSL(International Financial Services, London), Pension funds increased rapidly in recent year. Pension funds always have different ways to build up. One form always from the institutional investment and the funds will build up during the working life by the worker's company and then workers use the funds as the retirement income during workers retired. Alternatively some employees invest in a fund of their choosing and the money can be used to buy an annuity to obtain the pension funds. For this form, one of the important forms of stock market investments of pension funds is shares and bonds.展开更多
In this paper, we construct a general model for a pension fund when there are time delays in the valuation process. Actually, we use the standard structure of the basic reserve equation in order to rebuild a more soph...In this paper, we construct a general model for a pension fund when there are time delays in the valuation process. Actually, we use the standard structure of the basic reserve equation in order to rebuild a more sophisticated approach based on the theory of H<sub>∞</sub> control. Our model evaluates the incomplete information from the delayed fund valuations—due to the oscillatory pattern for benefit claims and investment experience of the past years—within the context of uncertainty additionally to the randomness which certainly exists. So, we construct estimations for the optimal proposed contribution rates based on a feedback mechanism which is a robust stabilization controller, using typical linear matrix inequalities. Finally, a numerical application is fully investigated to obtain further insight into the problem.展开更多
This paper studies a defined contribution(DC)pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment.In practice,most of pension plans were s...This paper studies a defined contribution(DC)pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment.In practice,most of pension plans were subject to the return of premiums clauses to protect the rights of pension members who died before retirement.In the mathematical modeling,we assume that a part of pension members could withdraw their premiums if they died before retirement and surviving members could equally share the difference between accumulated contributions and returned premiums.We suppose that the financial market consists of a risk-free asset,a stock,and a zero-coupon bond.The interest rate is driven by a stochastic affine interest rate model and the stock price follows the Heston’s stochastic volatility model with stochastic interest rates.Different fund managers have different risk preferences,and the hyperbolic absolute risk aversion(HARA)utility function is a general one including a power utility,an exponential utility,and a logarithm utility as special cases.We are concerned with an optimal portfolio to maximize the expected utility of terminal wealth by choosing the HARA utility function in the analysis.By using the principle of dynamic programming and Legendre transform-dual theory,we obtain explicit solutions of optimal strategies.Some special cases are also derived in detail.Finally,a numerical simulation is provided to illustrate our results.展开更多
This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security.First,we apply Ito?theorem to obtain the differential equation of the real sto...This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security.First,we apply Ito?theorem to obtain the differential equation of the real stock price after discounting inflation.Then,under the constraint of external guarantee of DC pension terminal wealth,self-protection is introduced to study the maximization of the expected utility of terminal wealth at retirement time and any time before retirement.The explicit solution of the optimal investment strategy of DC pension at retirement time and any time before retirement should be derived by martingale method.Finally,the influence of selfprotection on the optimal investment strategy of DC pension is numerically analyzed.展开更多
This paper investigates a multi-period portfolio optimization problem for a defined contribution pension plan with Telser's safety-first criterion.The plan members aim to maximize the expected terminal wealth subj...This paper investigates a multi-period portfolio optimization problem for a defined contribution pension plan with Telser's safety-first criterion.The plan members aim to maximize the expected terminal wealth subject to a constraint that the probability of the terminal wealth falling below a disaster level is less than a pre-determined number called risk control level.By Tchebycheff inequality,Lagrange multiplier technique,the embedding method and Bellman's principle of optimality,the authors obtain the conditions under which the optimal strategy exists and derive the closed-form optimal strategy and value function.Special cases show that the obtained results in this paper can be reduced to those in the classical mean-variance model.Finally,numerical analysis is provided to analyze the effects of the risk control level,the disaster level and the contribution proportion on the disaster probability and the value function.The numerical analysis indicates that the disaster probability in this paper is less than that in the classical mean-variance model on the premise that the value functions are the same in two models.展开更多
The establishment of individual accounts is the landmark events for China officially shift from pay-as-you-go pension system to partly funded system. But the process of running personal accounts at the same time also ...The establishment of individual accounts is the landmark events for China officially shift from pay-as-you-go pension system to partly funded system. But the process of running personal accounts at the same time also exposed various drawbacks. On the macro level, there is a growing gap between the nominal amount of personal account and the actual accumulated amount, which means the personal account is empty, the personal accounts are being questioned, and the scholars began to seek other solutions. NDC scheme came into being. specific empirical work has been done by using the actuarial model of pension income and expenditure to predict whether NDC is superior to FDC in financial cost by comparing the institutional cost of FDC and NDC from 2015 to 2050. Finally, this paper draws a conclusion that the nominal account system can be used as a choice route for the basic pension system for urban workers in the next 30 years with the assist of relevant supporting measures.展开更多
基金Supported by the National Natural Science Foundation of Tianjin (07JCYBJC05200)the Young Scholar Program of Tianjin University of Finance and Economics (TJYQ201201)
文摘In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.
文摘According to the data from IFSL(International Financial Services, London), Pension funds increased rapidly in recent year. Pension funds always have different ways to build up. One form always from the institutional investment and the funds will build up during the working life by the worker's company and then workers use the funds as the retirement income during workers retired. Alternatively some employees invest in a fund of their choosing and the money can be used to buy an annuity to obtain the pension funds. For this form, one of the important forms of stock market investments of pension funds is shares and bonds.
文摘In this paper, we construct a general model for a pension fund when there are time delays in the valuation process. Actually, we use the standard structure of the basic reserve equation in order to rebuild a more sophisticated approach based on the theory of H<sub>∞</sub> control. Our model evaluates the incomplete information from the delayed fund valuations—due to the oscillatory pattern for benefit claims and investment experience of the past years—within the context of uncertainty additionally to the randomness which certainly exists. So, we construct estimations for the optimal proposed contribution rates based on a feedback mechanism which is a robust stabilization controller, using typical linear matrix inequalities. Finally, a numerical application is fully investigated to obtain further insight into the problem.
基金supported by the National Social Science Foundation of China (No.21FJYB042)。
文摘This paper studies a defined contribution(DC)pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment.In practice,most of pension plans were subject to the return of premiums clauses to protect the rights of pension members who died before retirement.In the mathematical modeling,we assume that a part of pension members could withdraw their premiums if they died before retirement and surviving members could equally share the difference between accumulated contributions and returned premiums.We suppose that the financial market consists of a risk-free asset,a stock,and a zero-coupon bond.The interest rate is driven by a stochastic affine interest rate model and the stock price follows the Heston’s stochastic volatility model with stochastic interest rates.Different fund managers have different risk preferences,and the hyperbolic absolute risk aversion(HARA)utility function is a general one including a power utility,an exponential utility,and a logarithm utility as special cases.We are concerned with an optimal portfolio to maximize the expected utility of terminal wealth by choosing the HARA utility function in the analysis.By using the principle of dynamic programming and Legendre transform-dual theory,we obtain explicit solutions of optimal strategies.Some special cases are also derived in detail.Finally,a numerical simulation is provided to illustrate our results.
基金Supported by the National Social Science Foundation of China(20BTJ048)Anhui University Humanities and Social Science Research Major Project(SK2021ZD0043)。
文摘This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security.First,we apply Ito?theorem to obtain the differential equation of the real stock price after discounting inflation.Then,under the constraint of external guarantee of DC pension terminal wealth,self-protection is introduced to study the maximization of the expected utility of terminal wealth at retirement time and any time before retirement.The explicit solution of the optimal investment strategy of DC pension at retirement time and any time before retirement should be derived by martingale method.Finally,the influence of selfprotection on the optimal investment strategy of DC pension is numerically analyzed.
基金supported by grants from Innovation Research in Central University of Finance and Economics,National Natural Science Foundation of China under Grant Nos.11671411,71871071,72071051,Guangdong Basic and Applied Basic Research Foundation under Grant No.2018B030311004,the Key Program of the National Social Science Foundation of China under Grant No.21AZD071 and the 111 Project under Grant No.B17050.
文摘This paper investigates a multi-period portfolio optimization problem for a defined contribution pension plan with Telser's safety-first criterion.The plan members aim to maximize the expected terminal wealth subject to a constraint that the probability of the terminal wealth falling below a disaster level is less than a pre-determined number called risk control level.By Tchebycheff inequality,Lagrange multiplier technique,the embedding method and Bellman's principle of optimality,the authors obtain the conditions under which the optimal strategy exists and derive the closed-form optimal strategy and value function.Special cases show that the obtained results in this paper can be reduced to those in the classical mean-variance model.Finally,numerical analysis is provided to analyze the effects of the risk control level,the disaster level and the contribution proportion on the disaster probability and the value function.The numerical analysis indicates that the disaster probability in this paper is less than that in the classical mean-variance model on the premise that the value functions are the same in two models.
文摘The establishment of individual accounts is the landmark events for China officially shift from pay-as-you-go pension system to partly funded system. But the process of running personal accounts at the same time also exposed various drawbacks. On the macro level, there is a growing gap between the nominal amount of personal account and the actual accumulated amount, which means the personal account is empty, the personal accounts are being questioned, and the scholars began to seek other solutions. NDC scheme came into being. specific empirical work has been done by using the actuarial model of pension income and expenditure to predict whether NDC is superior to FDC in financial cost by comparing the institutional cost of FDC and NDC from 2015 to 2050. Finally, this paper draws a conclusion that the nominal account system can be used as a choice route for the basic pension system for urban workers in the next 30 years with the assist of relevant supporting measures.
