Deep Pricing Kernels for Constrained Life-Cycle Portfolio Optimization

Summary

This paper studies portfolio choice over an individual’s life when income is stochastic and investments include stocks, a bond, and life insurance. The objective accounts for consumption, death benefits, and terminal wealth. A convex trading constraint represents restrictions such as assets that cannot be traded, bans on short selling, or limits on borrowing.

The authors construct artificial markets by adjusting compensated asset drifts so that the resulting market reflects the trading constraints. They then use a dual transformation and a deep pricing-kernel method to calculate lower and upper bounds on the original optimization problem. This approach is intended for cases where the value function cannot be written explicitly because the pricing kernel involves a conditional expectation. The stated conclusion is that constraints reduce consumption, life-insurance and annuity demand, and wealth. The abstract does not provide numerical results, specify the tightness achieved by the bounds, or detail how performance varies across constraint types.

Key ideas

• The life-cycle model combines stochastic income, financial assets, life insurance, consumption, death benefits, and terminal wealth.
• A convex trading constraint can represent limits on trading, short selling, or borrowing.
• Artificial markets incorporate constraints through changes to compensated asset drifts.
• A dual deep pricing-kernel method estimates lower and upper bounds when explicit value functions are unavailable.
• The paper reports lower consumption, insurance and annuity demand, and wealth under trading constraints.

Tags

# Constrained portfolio optimization in a life-cycle model: A deep pricing kernel approach


# Constrained portfolio optimization in a life-cycle model: A deep pricing kernel approach









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 their consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, with the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint as special cases. We build the artificial markets to solve this problem by manipulating the compensated drift terms of the underlying assets to meet the trading constraints. By dual transform, we propose a deep pricing kernel approach to compute tight lower and upper bounds for the primal problem, which can be used when the value function lacks an explicit solution due to the pricing kernel's conditional expectation. Finally, we conclude that when considering the trading constraints, the individual will reduce their consumption, demand for life insurance and annuities, and wealth levels due to the restricted market.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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