Stochastic pension fund control in the presence of Poisson jumps.

*(English)*Zbl 1120.60063Summary: We consider the problem of optimal funding and asset allocation for a defined benefit pension scheme by assuming that the pension fund can be invested in a risk-free asset and a risky asset whose return follows a jump diffusion process. We extend existing literature which mainly assumes that the risky asset’s return follows a pure diffusion process. In a stochastic analysis of the optimal policies we show that the optimal contribution and asset allocation policies have similar forms as in the pure diffusion approaches, but with a modification for the effect of jumps. These results hold under both constant pension scheme benefit outgo and stochastic pension scheme benefit outgo. Using a sensitivity analysis of the effect of the mean jump magnitude on the asset allocation policy, we show that increasing (in absolute terms) the mean jump magnitude reduces the allocation in the risky asset and increases the allocation in the risk-free asset.

##### MSC:

60H30 | Applications of stochastic analysis (to PDEs, etc.) |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

91G10 | Portfolio theory |

93E20 | Optimal stochastic control |

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\textit{B. Ngwira} and \textit{R. Gerrard}, Insur. Math. Econ. 40, No. 2, 283--292 (2007; Zbl 1120.60063)

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##### References:

[1] | Cairns, A.J.G., Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time, Astin bulletin, 30, 1, 19-55, (2000) · Zbl 1018.91028 |

[2] | Chang, S.C.; Tzeng, L.Y.; Miao, J.C.Y., Pension funding incorporating downside risks, Insurance: mathematics and economics, 32, 217-228, (2003) · Zbl 1074.91547 |

[3] | Das, S.R.; Uppal, R., Systemic risk and international portfolio choice, The journal of finance, 59, 2809-2834, (2004) |

[4] | Haberman, S.; Day, C.; Fogarty, D.; Khorasanee, M.Z.; McWhirter, M.; Nash, N.; Ngwira, B.; Wright, I.D.; Yakoubov, Y., A stochastic approach to risk management and decision-making in defined benefit pension schemes (with discussion), British actuarial journal, 9, 3, 493-618, (2003) |

[5] | Josa-Fombellida, R.; Rincón-Zapatero, J.P., Minimization of risks in pension funding by means of contributions and portfolio selection, Insurance: mathematics and economics, 29, 35-45, (2001) · Zbl 1055.91051 |

[6] | Josa-Fombellida, R.; Rincón-Zapatero, J.P., Optimal risk management in defined benefit stochastic pension funds, Insurance: mathematics and economics, 34, 489-503, (2004) · Zbl 1188.91202 |

[7] | Liu, J.; Longstaff, F.R.; Pan, J., Dynamic asset allocation with event risk, The journal of finance, 58, 231-259, (2003) |

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

[9] | Owadally, M.I.; Haberman, S., Efficient gain and loss amortization and optimal funding in pension plans, North American actuarial journal, 8, 21-36, (2004) · Zbl 1085.62509 |

[10] | Sung, J.-H., 1997. Dynamic programming approaches to pension funding. Ph.D. Thesis, The City University, London |

[11] | Wu, L., Jumps and dynamic asset allocation, Review of quantitative finance and accounting, 20, 207-243, (2003) |

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