Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Dynamic Coalition Portfolio Selection with Recursive Utility

Hanxiao Wang, Chao Zhou

Abstract

In this paper, we consider a dynamic coalition portfolio selection problem, with each agent's objective given by an Epstein--Zin recursive utility. To find a Pareto optimum, the coalition's problem is formulated as an optimization problem evolved by a multi-dimensional forward-backward SDE. Since the evolution system has a forward-backward structure, the problem is intrinsically time-inconsistent. With the dynamic-game point of view, we rigorously develop an approach to finding the equilibrium Pareto investment-consumption strategy. We find that the relationship between risk aversion and EIS has more influence on the coalition's problem than that on the one-agent problem. More interestingly, we show that the equilibrium Pareto consumption strategy associated with the recursive utility is much more effective than that associated with the CRRA expected utility, which highlights the feature of recursive utilities that the marginal benefit of consumption can depend on the future consumption.

Dynamic Coalition Portfolio Selection with Recursive Utility

Abstract

In this paper, we consider a dynamic coalition portfolio selection problem, with each agent's objective given by an Epstein--Zin recursive utility. To find a Pareto optimum, the coalition's problem is formulated as an optimization problem evolved by a multi-dimensional forward-backward SDE. Since the evolution system has a forward-backward structure, the problem is intrinsically time-inconsistent. With the dynamic-game point of view, we rigorously develop an approach to finding the equilibrium Pareto investment-consumption strategy. We find that the relationship between risk aversion and EIS has more influence on the coalition's problem than that on the one-agent problem. More interestingly, we show that the equilibrium Pareto consumption strategy associated with the recursive utility is much more effective than that associated with the CRRA expected utility, which highlights the feature of recursive utilities that the marginal benefit of consumption can depend on the future consumption.
Paper Structure (15 sections, 5 theorems, 104 equations, 2 figures)

This paper contains 15 sections, 5 theorems, 104 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Literature review on recursive coalition problem
  3. Literature review on optimal control theory for FBSDEs
  4. Literature review on time-inconsistent control theory
  5. The model and problem formulation
  6. Time-inconsistency of the model
  7. The main result
  8. Equilibrium Pareto strategy
  9. Equilibrium HJB equation: Verification theorem and well-posedness
  10. Interpretation and numerics
  11. Monotonic property of equilibrium consumption strategy
  12. Comparison with one-agent model
  13. Comparison with CRRA model
  14. Numerics
  15. Appendix: Proof of the main results

Key Result

Proposition 2.1

Under the assumptions presented above, the following ODE admits a unique positive solution: Moreover, is a solution to M-BSDE.

Figures (2)

  • Figure 1: The case with $\gamma\in(0,1-\alpha)$.
  • Figure 2: The case with $\gamma\in(1-\alpha,1)$.

Theorems & Definitions (10)

  • Proposition 2.1
  • Definition 2.2
  • Definition 4.1
  • Remark 4.2
  • Remark 4.3
  • Theorem 4.4
  • Theorem 4.5
  • Corollary 4.6
  • Proposition 5.1
  • proof