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Time-consistent pension policy with minimum guarantee and sustainability constraint

Caroline Hillairet, Sarah Kaakai, Mohamed Mrad

Abstract

This paper proposes and investigates an optimal pair investment/pension policy for a pay-as-you-go (PAYG) pension scheme. The social planner can invest in a buffer fund in order to guarantee a minimal pension amount. The model aims at taking into account complex dynamic phenomena such as the demographic risk and its evolution over time, the time and age dependence of agents preferences, and financial risks. The preference criterion of the social planner is modeled by a consistent dynamic utility defined on a stochastic domain, which incorporates the heterogeneity of overlapping generations and its evolution over time. The preference criterion and the optimization problem also incorporate sustainability, adequacy and fairness constraints. The paper designs and solves the social planner's dynamic decision criterion, and computes the optimal investment/pension policy in a general framework. A detailed analysis for the case of dynamic power utilities is provided.

Time-consistent pension policy with minimum guarantee and sustainability constraint

Abstract

This paper proposes and investigates an optimal pair investment/pension policy for a pay-as-you-go (PAYG) pension scheme. The social planner can invest in a buffer fund in order to guarantee a minimal pension amount. The model aims at taking into account complex dynamic phenomena such as the demographic risk and its evolution over time, the time and age dependence of agents preferences, and financial risks. The preference criterion of the social planner is modeled by a consistent dynamic utility defined on a stochastic domain, which incorporates the heterogeneity of overlapping generations and its evolution over time. The preference criterion and the optimization problem also incorporate sustainability, adequacy and fairness constraints. The paper designs and solves the social planner's dynamic decision criterion, and computes the optimal investment/pension policy in a general framework. A detailed analysis for the case of dynamic power utilities is provided.
Paper Structure (32 sections, 10 theorems, 107 equations)

This paper contains 32 sections, 10 theorems, 107 equations.

Table of Contents

  1. The model
  2. Population dynamics
  3. Pension system
  4. Contribution process
  5. Pension process and adequacy constraint
  6. Buffer fund
  7. Financial market
  8. Investment in the buffer fund
  9. Social planner strategy
  10. The social planner's dynamic decision criterion
  11. Definition of Dynamic Utilities
  12. Dynamic CRRA utilities
  13. Buffer fund and pensioners dynamic utilities
  14. Consistency Property
  15. Consistency and optimal strategy
  16. ...and 17 more sections

Key Result

Proposition 2.9

Recall that the bound $\mathfrak{K}_t$ is an Itô process with dynamics $d\mathfrak{K}_t = \mu_t^\mathfrak{K} dt + \delta_t^\mathfrak{K}\cdot dW_t$. Under Assumption HypBarU, $U$ is a dynamic utility on the domain $\mathcal{D}_U = \{ (\omega,t,z), \; z \geq \mathfrak{K}_t \}$, with local character

Theorems & Definitions (31)

  • Example 1
  • Example 2
  • Definition 1.1: Admissible strategy
  • Definition 1.2
  • Definition 2.1: Dynamic Utility on stochastic domain
  • Remark 2.2
  • Definition 2.3
  • Definition 2.4: Buffer fund utility
  • Definition 2.5: Pensioners' utility
  • Definition 2.7: Consistent dynamic utility
  • ...and 21 more