## Optimal dynamic asset allocation for DC plan accumulation/decumulation: ambition-CVaR.(English)Zbl 1447.91137

Summary: We consider the late accumulation stage, followed by the full decumulation stage, of an investor in a defined contribution (DC) pension plan. The investor’s portfolio consists of a stock index and a bond index. As a measure of risk, we use conditional value at risk (CVaR) at the end of the decumulation stage. This is a measure of the risk of depleting the DC plan, which is primarily driven by sequence of return risk and asset allocation during the decumulation stage. As a measure of reward, we use Ambition, which we define to be the probability that the terminal wealth exceeds a specified level. We develop a method for computing the optimal dynamic asset allocation strategy which generates points on the efficient ambition-CVaR frontier. By examining the ambition-CVaR efficient frontier, we can determine points that are median-CVaR optimal. We carry out numerical tests comparing the median-CVaR optimal strategy to a benchmark constant proportion strategy. For a fixed median value (from the benchmark strategy) we find that the optimal median-CVaR control significantly improves the CVaR. In addition, the median allocation to stocks at retirement is considerably smaller than the benchmark allocation to stocks.

### MSC:

 91G05 Actuarial mathematics 91G10 Portfolio theory 91G70 Statistical methods; risk measures
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