**DISCUSSION PAPER PI-0818**

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.