##
**Stochastic lifestyling: optimal dynamic asset allocation for defined contribution pension plans.**
*(English)*
Zbl 1200.91297

Summary: We investigate asset-allocation strategies open to members of defined-contribution pension plans with a model that incorporates asset, salary (labour-income) and interest-rate risk. We propose a novel form of terminal utility function, incorporating habit formation, that uses the member’s final salary as a numeraire. The paper discusses various properties and characteristics of the optimal asset-allocation strategy both with and without the presence of non-hedgeable salary risk. Finally, we compare the performance of the optimal strategy with some popular alternatives used by pension providers and we conclude that it significantly enhances the welfare of a wide range of potential plan members relative to these other strategies.

### MSC:

91G50 | Corporate finance (dividends, real options, etc.) |

93E20 | Optimal stochastic control |

91B30 | Risk theory, insurance (MSC2010) |

91G10 | Portfolio theory |

### Keywords:

stochastic control; optimal asset allocation; stochastic lifestyling; utility numeraire; habit formation; non-hedgeable salary risk; HJB equation
PDF
BibTeX
XML
Cite

\textit{A. J. G. Cairns} et al., J. Econ. Dyn. Control 30, No. 5, 843--877 (2006; Zbl 1200.91297)

### References:

[1] | Ando, A.; Modigliani, F., The ‘life cycle’ hypothesis of saving: aggregate implications and tests, American economic review, 53, 55-84, (1963) |

[2] | Björk, T., Arbitrage in theory in continuous time, (1998), OUP Oxford |

[3] | Black, F.; Jones, R., Simplifying portfolio insurance for corporate pension plans, Journal of portfolio management, 14, 33-37, (1988) |

[4] | Black, F.; Perold, A., Theory of constant proportion portfolio insurance, Journal of economic dynamics and control, 16, 403-426, (1992) · Zbl 0825.90056 |

[5] | Blake, D.; Cairns, A.J.G.; Dowd, K., Pensionmetrics I: stochastic pension plan design and value at risk during the accumulation phase, Insurance: mathematics and economics, 29, 187-215, (2001) · Zbl 0989.62057 |

[6] | Boulier, J.-F.; Huang, S.-J.; Taillard, G., Optimal management under stochastic interest rates: the case of a protected pension fund, Insurance: mathematics and economics, 28, 173-189, (2001) · Zbl 0976.91034 |

[7] | Cairns, A.J.G., Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time, ASTIN bulletin, 30, 19-55, (2000) · Zbl 1018.91028 |

[8] | Constantinides, G.M., Habit formation: a resolution of the equity premium puzzle, The journal of political economy, 98, 519-543, (1990) |

[9] | Cox, J.C.; Huang, C.-F., A variational problem arising in financial economics, Journal of mathematical economics, 20, 465-487, (1991) · Zbl 0734.90009 |

[10] | Deelstra, G.; Grasselli, M.; Koehl, P.-F., Optimal investment strategies in a CIR framework, Journal of applied probability, 37, 936-946, (2000) · Zbl 0989.91040 |

[11] | Duffie, D.; Fleming, W.; Soner, H.M.; Zariphopoulou, T., Hedging in incomplete markets with HARA utility, Journal of economic dynamics and control, 21, 753-782, (1997) · Zbl 0899.90026 |

[12] | Epstein, L.G.; Zin, S.E., Substitution, risk aversion, and the temporal behavior of consumption and asset returns: a theoretical framework, Econometrica, 57, 937-969, (1989) · Zbl 0683.90012 |

[13] | Gollier, C., Pratt, J.W., 1996. Risk vulnerability and the tempering effect of background risk. Econometrica 64, 1109-1123. · Zbl 0856.90014 |

[14] | Karatzas, I.; Lehoczky, J.P.; Shreve, S.E., Optimal portfolio and consumption decisions for a small investor on a finite horizon, SIAM journal of control and optimization, 25, 1557-1586, (1987) · Zbl 0644.93066 |

[15] | Kimball, M.S., 1993. Standard risk aversion. Econometrica 61, 589-611. · Zbl 0771.90017 |

[16] | Korn, R., Optimal portfolios, (1997), World Scientific Singapore |

[17] | Korn, R., Krekel, M., 2002. Optimal portfolios with fixed consumption and income streams. Working Paper, University of Kaiserslautern. |

[18] | Liu, J., 2005. Portfolio selection in stochastic environments. Working Paper, Anderson School of Management, UCLA. |

[19] | Malkiel, B.G., A random walk down wall street, (2003), Norton New York |

[20] | Merton, R.C., Lifetime portfolio selection under uncertainty: the continuous-time case, Review of economics and statistics, 51, 247-257, (1969) |

[21] | Merton, R.C., Optimum consumption and portfolio rules in a continuous-time model, Journal of economic theory, 3, 373-413, (1971) · Zbl 1011.91502 |

[22] | Merton, R.C., Continuous-time in finance, (1990), Blackwell Cambridge, MA |

[23] | Øksendal, B., Stochastic in differential equations, (1998), Springer Berlin |

[24] | Pratt, J.W., Zeckhauser, R.J., 1987. Proper risk aversion. Econometrica 55, 143-154. · Zbl 0612.90006 |

[25] | Ryder, H.E.; Heal, G.M., Optimum growth with intertemporally dependent preferences, Review of economic studies, 40, 1-33, (1973) · Zbl 0261.90007 |

[26] | Sundaresan, S.M., Intertemporally dependent preferences and the volatility of consumption and wealth, Review of financial studies, 2, 73-89, (1989) |

[27] | Sundaresan, S.; Zapatero, F., Valuation, optimal asset allocation and retirement incentives of pension plans, Review of financial studies, 10, 631-660, (1997) |

[28] | Vasicek, O.E., An equilibrium characterisation of the term structure, Journal of financial economics, 5, 177-188, (1977) · Zbl 1372.91113 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.