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Inter-temporal optimization and deterministic lifestyle strategy in managing defined-contribution
pension plans

Qing-Ping Ma

Inter-temporal optimization and deterministic lifestyle asset allocation
strategies for defined-contribution pension plans are investigated and compared both
analytically and numerically. The pension plan is assumed to invest in two types of
asset, risk free assets and equities, or bonds and equities, and the plan members’
terminal utility a power function of pension wealth at retirement with their final
wages as numeraire. The optimal asset allocation strategy using two assets is derived
analytically for fully hedgeable wage incomes and compared numerically with that for
non-hedgeable wage income and deterministic lifestyle strategy. The deterministic
lifestyle strategy is shown to be replicable by a static allocation strategy with same
expected returns and lower variances. The inter-temporal optimization strategy
outperforms the lifestyle strategy in numerical simulations both when there is no
further pension contribution or non-hedgeable wage risk and when the wage income is
not fully hedgeable. When there are further pension contributions, the optimal
proportion invested in the more risky asset is higher than that when future pension
contributions are transformed into augmented wealth by short-selling a replicating
portfolio to be paid by future pension contributions. With usual assumptions on
market parameters, the optimal pension portfolio composition is independent of the
value of non-hedgeble wage risk and the value of pension contribution rate.

Keywords : Optimal asset allocation; Defined-contribution pension plan; Lifestyle;
Power utility; Hamilton-Jacobi-Bellman equation; wage risk.