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CN 34-1054/N

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Optimal investment of DC pension under the inflation and loss aversion

  • Department of Financial Engineering, School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China

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https://doi.org/10.3969/j.issn.0253-2778.2018.05.011
  • Received Date: 23 July 2017
  • Accepted Date: 15 December 2017
  • Rev Recd Date: 15 December 2017
  • Publish Date: 31 May 2018
    Abstract

  • Abstract

    The optimal investment problem of DC pension under the inflation and loss aversion was studied.First， the stochastic differential equation of the real stock price after inflation was discounted by the Ito formula. Then， in the framework of prospect theory， considering the problem of maximizing the expected utility of terminal wealth discounted by inflation at retirement， the explicit solution of the optimal investment strategy of DC pension at any time before retirement was derived by using the martingale method.In the end， the impact of the loss aversion on the optimal investment strategy of DC pension was analyzed using the Monte-Carlo method.

    Abstract

    The optimal investment problem of DC pension under the inflation and loss aversion was studied.First， the stochastic differential equation of the real stock price after inflation was discounted by the Ito formula. Then， in the framework of prospect theory， considering the problem of maximizing the expected utility of terminal wealth discounted by inflation at retirement， the explicit solution of the optimal investment strategy of DC pension at any time before retirement was derived by using the martingale method.In the end， the impact of the loss aversion on the optimal investment strategy of DC pension was analyzed using the Monte-Carlo method.
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    • References(15)
  • [1]
    VIGNA E, HABERMAN S. Optimal investment strategy for defined contribution pension schemes[J]. Insurance: Mathematics and Economics, 2001, 28: 233-262.
    [2]
    BOULIER J F, HUANG S J, TAILLARD G. Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund[J]. Insurance: Mathematics and Economics, 2001, 28: 173-189.
    [3]
    GUAN G, LIANG Z. Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework[J]. Insurance: Mathematics and Economics, 2014, 57: 58-66.
    [4]
    BATTOCCHIO P, MENONCIN F. Optimal pension management in a stochastic framework[J]. Insurance: Mathematics and Economics, 2004, 34: 79- 95.
    [5]
    MUNK C, SRENSEN C, VINTHER T N. Dynamic asset allocation under mean-reverting returns, stochastic interest rates and inflation uncertainty are popular recommendations consistent with rational behavior?[J]. International Review of Economics and Finance, 2004, 13: 141-166.
    [6]
    HAN N W, HUNG M W. Optimal asset allocation for DC pension plans under inflation[J]. Insurance: Mathematics and Economics, 2012, 51: 172-181.
    [7]
    YAO H X, YANG Z, CHEN P. Markowitzs mean-variance defined contribution pension fund management under inflation: A continuous-time model[J]. Insurance: Mathematics and Economics, 2013, 53: 851-863.
    [8]
    殷俊, 李媛媛. 基于随机利率和通货膨胀的缴费确定型养老金计划最优资产配置策略[J]. 当代经济科学, 2013, 35 (2): 11-21.
    YIN Jun，LI Yuanyuan. Stochastic interest rate and inflation based optimal asset allocation tactics for defined-contribution pension plans[J].Modern Economic Science, 2013, 35 (2): 11-21.
    [9]
    KAHNEMAN D, TVERSKY A. Prospect theory: An analysis of decision under risk[J]. Econometrica, 1979, 47(2): 263-292.
    [10]
    BERKELAAR A B, KOUWENBERG R, POST T. Optimal portfolio choice under loss aversion[J]. Rev Econ Stat, 2004, 86 (4): 973-987.
    [11]
    GOMES F J. Portfolio choice and trading volume with loss-averse investors[J]. J Bus, 2005, 78 (2): 675-706.
    [12]
    GUAN G, LIANG Z. Optimal management of DC pension plan under loss aversion and value-at-risk constraints[J]. Insurance: Mathematics and Economics, 2016, 69: 224-237.
    [13]
    费为银, 李允贺, 夏登峰. 通胀下带激励的对冲基金最优投资[J]. 系统工程理论与实践, 2015, 35(11): 2740-2748.
    FEI Weiyin, LI Yunhe, XIA Dengfeng. Optimal investment strategies of hedge funds with incentive fees under inflationary environment[J]. Systems Engineering： Theory & Practice, 2015, 35(11): 2740-2748.
    [14]
    COX J, HUANG C. Optimum consumption and portfolio policies when asset prices follow a diffusion process[J]. Journal of Economic Theory, 1989, 49: 33-83.
    [15]
    DEELSTRA G, GRASSELLI M, KOEHL P F. Optimal investment strategies in the presence of a minimum guarantee[J]. Insurance: Mathematics and Economics, 2003, 33: 189-207.
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    [1]
    VIGNA E, HABERMAN S. Optimal investment strategy for defined contribution pension schemes[J]. Insurance: Mathematics and Economics, 2001, 28: 233-262.
    [2]
    BOULIER J F, HUANG S J, TAILLARD G. Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund[J]. Insurance: Mathematics and Economics, 2001, 28: 173-189.
    [3]
    GUAN G, LIANG Z. Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework[J]. Insurance: Mathematics and Economics, 2014, 57: 58-66.
    [4]
    BATTOCCHIO P, MENONCIN F. Optimal pension management in a stochastic framework[J]. Insurance: Mathematics and Economics, 2004, 34: 79- 95.
    [5]
    MUNK C, SRENSEN C, VINTHER T N. Dynamic asset allocation under mean-reverting returns, stochastic interest rates and inflation uncertainty are popular recommendations consistent with rational behavior?[J]. International Review of Economics and Finance, 2004, 13: 141-166.
    [6]
    HAN N W, HUNG M W. Optimal asset allocation for DC pension plans under inflation[J]. Insurance: Mathematics and Economics, 2012, 51: 172-181.
    [7]
    YAO H X, YANG Z, CHEN P. Markowitzs mean-variance defined contribution pension fund management under inflation: A continuous-time model[J]. Insurance: Mathematics and Economics, 2013, 53: 851-863.
    [8]
    殷俊, 李媛媛. 基于随机利率和通货膨胀的缴费确定型养老金计划最优资产配置策略[J]. 当代经济科学, 2013, 35 (2): 11-21.
    YIN Jun，LI Yuanyuan. Stochastic interest rate and inflation based optimal asset allocation tactics for defined-contribution pension plans[J].Modern Economic Science, 2013, 35 (2): 11-21.
    [9]
    KAHNEMAN D, TVERSKY A. Prospect theory: An analysis of decision under risk[J]. Econometrica, 1979, 47(2): 263-292.
    [10]
    BERKELAAR A B, KOUWENBERG R, POST T. Optimal portfolio choice under loss aversion[J]. Rev Econ Stat, 2004, 86 (4): 973-987.
    [11]
    GOMES F J. Portfolio choice and trading volume with loss-averse investors[J]. J Bus, 2005, 78 (2): 675-706.
    [12]
    GUAN G, LIANG Z. Optimal management of DC pension plan under loss aversion and value-at-risk constraints[J]. Insurance: Mathematics and Economics, 2016, 69: 224-237.
    [13]
    费为银, 李允贺, 夏登峰. 通胀下带激励的对冲基金最优投资[J]. 系统工程理论与实践, 2015, 35(11): 2740-2748.
    FEI Weiyin, LI Yunhe, XIA Dengfeng. Optimal investment strategies of hedge funds with incentive fees under inflationary environment[J]. Systems Engineering： Theory & Practice, 2015, 35(11): 2740-2748.
    [14]
    COX J, HUANG C. Optimum consumption and portfolio policies when asset prices follow a diffusion process[J]. Journal of Economic Theory, 1989, 49: 33-83.
    [15]
    DEELSTRA G, GRASSELLI M, KOEHL P F. Optimal investment strategies in the presence of a minimum guarantee[J]. Insurance: Mathematics and Economics, 2003, 33: 189-207.
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