Scenario-Tree Dynamic Programming for Target-Date Asset Allocation

Summary

This article introduces discrete-time stochastic control as a method for dynamic asset allocation. Unlike a traditional mean-variance allocation made without an explicit sequence of future decisions, the approach models portfolio choices across multiple periods and maximizes a specified utility objective under changing asset values. It contrasts this with continuous-time control, which models returns through stochastic differential equations and typically requires numerical methods to solve the associated Hamilton-Jacobi-Bellman equation.

For computation, the article describes scenario trees as a way to approximate continuous outcomes with discrete states, then uses simulation and multi-stage dynamic programming to select allocations. Its example considers a four-quarter horizon with stocks represented by a Chinese equity index and bonds by a Chinese bond wealth index, using three possible future scenarios. Scenarios may be generated through Monte Carlo simulation, judgment, or both. The text outlines the setup but does not include the referenced detailed table or the numerical allocation results, and scenario design and optimization remain important limits.

Key ideas

• Discrete-time stochastic control chooses allocations across multiple periods to optimize a utility objective.
• Continuous-time approaches model returns with stochastic differential equations and often need numerical solutions.
• Scenario trees approximate uncertain outcomes with discrete states for dynamic programming.
• The example models quarterly allocation between Chinese stock and bond indices over a one-year horizon.
• Scenario assumptions can come from simulation, judgment, or a combination of both.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.