The curse of dimensionality describes how dynamic programming becomes difficult as financial planning models add wealth states, state variables, and possible actions. A dynamic program must evaluate every state–action combination, so computational requirements can grow rapidly. section 6.2.1
In a small goals-based investing problem, dynamic programming can finish in seconds because the state and action spaces are limited. More realistic wealth problems require more states and actions, including many highly unlikely paths that exact backward recursion still evaluates. section 6.2.1
The practical consequence is a trade-off between exact dynamic programming and simulation-based reinforcement learning:
- Dynamic programming computes the value function by looping through every state and action and requires transition probabilities. section 6.2.1
- Reinforcement learning moves forward through time and approximates the value function by simulating more likely paths rather than enumerating every possible path. section 6.2.1
- Adding labor income, health expenses, taxes, housing decisions, bequests, or alternative utility functions can expand the planning model further. section 6.6
Goals-based investing
A dynamic program stores values for wealth states across time, evaluates each of 21 asset-allocation actions, and selects the action with the greatest expected value. Increasing the number of wealth states, actions, or financial variables multiplies this computation.
