Portfolio optimization in DC pension scheme with unhedgeable stochastic wage

Francesco Menoncin and Elena Vigna

Carlo Alberto Notebooks from Collegio Carlo Alberto

Abstract: We solve a dynamic portfolio optimization problem in the accumulation phase of a defined contribution (DC) pension plan with a stochastic wage driven by a non-hedgeable random source. The incomplete financial market consists of a riskfree and a risky assets, and the stochastic wage has non-zero correlation with the risky asset. The optimization problem defined with a constant absolute risk aversion (CARA) utility function is solved via dynamic programming in closed form with constant riskfree interest rate and constant correlation between wage and risky asset. We also show that the application of the martingale approach provides an approximated solution based on the least square method, and we highlight the difference between the optimal and the approximated solutions. A numerical application investigates (i) the impact on the optimal investment strategy of the correlation between wage and risky asset, (ii) the comparison with the complete market case, and (iii) the relationship between the optimal and the approximated solutions. The main conclusion drawn is that failing to model the imperfect correlation between wage and risky asset in a DC pension scheme leads to investment policies that are far away the optimal ones, and to distorted outcomes in terms of final wealth.

Keywords: DC pension scheme; incomplete market; stochastic wage; dynamic programming; optimal portfolio (search for similar items in EconPapers)
Pages: 29 pages
Date: 2025
New Economics Papers: this item is included in nep-age and nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:cca:wpaper:740

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