Mean-Variance Portfolio Selection Problem with Stochastic Salary for a Defined Contribution Pension Scheme: A Stochastic Linear-Quadratic-Exponential Framework
Abstract:This paper examines a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a defined contribution (DC) pension plan. The utility function is assumed to be quadratic. It was assumed that the flow of contributions made by the pension plan members (PPMs) are invested into a market that is characterized by a cash account, an inflation-linked bond and a stock. In this paper, inflation-linked bond is traded and used to hedge inflation risks a… Show more
“…In solving (10), we set ω = ϕ 2ψ and V (t) = X(t) − ω, See [18] for details. As already explained in [18], the problem is equivalent to solving…”
Section: The Optimization Problemmentioning
confidence: 99%
“…There have been many studies on the maximization of expected utility of terminal wealth of PPMs in the accumulation phase of defined contribution pension schemes. See, for example, [7,14,4,2,5,9,11,10,8,16,17,18].…”
Section: Introductionmentioning
confidence: 99%
“…Closely related to this article is a paper by [18], who studied a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a DC pension plan. The flow of contribution made by PPMs was assumed to be invested into a market that is characterized by a cash account, an inflation-linked bond and a stock.…”
Section: Introductionmentioning
confidence: 99%
“…In the paper, efficient frontier was found to be parabolic in shape, due to the present of initial capital and the existence of stochastic contributions of the PPM. But, [18] do not addressed wealth and portfolio process with proportional administrative costs and taxation, which we intend to address in this paper. In this paper, administrative cost are those cost incurred in the day-to-day running of the scheme.…”
This paper aim at studying a mean-variance portfolio selection problem with stochastic salary, proportional administrative costs and taxation in the accumulation phase of a defined contribution (DC) pension scheme. The fund process is subjected to taxation while the contribution of the pension plan member (PPM) is tax exempt. It is assumed that the flow of contributions of a PPM are invested into a market that is characterized by a cash account and a stock. The optimal portfolio processes and expected wealth for the PPM are established. The efficient and parabolic frontiers of a PPM portfolios in mean-variance are obtained. It was found that capital market line can be attained when initial fund and the contribution rate are zero. It was also found that the optimal portfolio process involved an inter-temporal hedging term that will offset any shocks to the stochastic salary of the PPM.
“…In solving (10), we set ω = ϕ 2ψ and V (t) = X(t) − ω, See [18] for details. As already explained in [18], the problem is equivalent to solving…”
Section: The Optimization Problemmentioning
confidence: 99%
“…There have been many studies on the maximization of expected utility of terminal wealth of PPMs in the accumulation phase of defined contribution pension schemes. See, for example, [7,14,4,2,5,9,11,10,8,16,17,18].…”
Section: Introductionmentioning
confidence: 99%
“…Closely related to this article is a paper by [18], who studied a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a DC pension plan. The flow of contribution made by PPMs was assumed to be invested into a market that is characterized by a cash account, an inflation-linked bond and a stock.…”
Section: Introductionmentioning
confidence: 99%
“…In the paper, efficient frontier was found to be parabolic in shape, due to the present of initial capital and the existence of stochastic contributions of the PPM. But, [18] do not addressed wealth and portfolio process with proportional administrative costs and taxation, which we intend to address in this paper. In this paper, administrative cost are those cost incurred in the day-to-day running of the scheme.…”
This paper aim at studying a mean-variance portfolio selection problem with stochastic salary, proportional administrative costs and taxation in the accumulation phase of a defined contribution (DC) pension scheme. The fund process is subjected to taxation while the contribution of the pension plan member (PPM) is tax exempt. It is assumed that the flow of contributions of a PPM are invested into a market that is characterized by a cash account and a stock. The optimal portfolio processes and expected wealth for the PPM are established. The efficient and parabolic frontiers of a PPM portfolios in mean-variance are obtained. It was found that capital market line can be attained when initial fund and the contribution rate are zero. It was also found that the optimal portfolio process involved an inter-temporal hedging term that will offset any shocks to the stochastic salary of the PPM.
“…Højgaad and Vigna (2007) compare a mean-variance model with a target-based model, and show that the target-based model can be formulated as a meanvariance model. Nkeki (2013) studies a mean-variance DC pension management problem with time-dependent salary, and compares the optimal portfolios under quadratic utility function, power utility function and exponential utility function. He and Liang (2013) introduce the return of premium clauses into the portfolio model with the mean-variance criterion for a DC pension plan during the accumulation phase, and derive a time-consistent investment strategy within the game theoretic framework.…”
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