Constrained portfolio optimization in a life-cycle model

TL;DR

This paper develops a dual control neural network method for constrained portfolio optimization in a life-cycle model, extending existing theories and analyzing the impact of trading constraints on insurance demand.

Contribution

It introduces a neural network approach to solve complex constrained portfolio problems and extends duality theory to more general income and interest rate conditions.

Findings

Trading constraints reduce life insurance demand.

Dual control neural network provides tight bounds for optimization.

Extended theoretical framework for life-cycle investment models.

Abstract

This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, of which the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint are special cases. Following Cuoco (1997), we build the artificial markets to derive the dual problem and prove the existence of the original problem. With additional discussions, we extend his uniformly bounded assumption on the interest rate to an almost surely finite expectation condition and enlarge his uniformly bounded assumption on the income process to a bounded expectation condition. Moreover, we propose a dual control neural network approach to compute tight lower and upper bounds for the original problem, which can be utilized in more general cases than the simulation of artificial markets strategies (SAMS) approach in Bick et al. (2013). Finally, we conclude that when considering the trading constraints, the individual will reduce his or her demand for life insurance.