Framing Dynamic Programming for Investment Strategy Search

Summary

The document frames an optimization problem: selecting asset allocations across successive decades over a century, using a restricted set of choices among equities, cash, and bonds. Each period permits either a full allocation to one asset or an equal split between two, with the entire portfolio invested. The author has searched for suitable strategies using a genetic algorithm that progressively considers larger time blocks, but is looking for a more principled approach to the large decision space.

A candidate strategy is evaluated by simulating fund outcomes and comparing the resulting quantiles with specified criteria. The author considers Bellman’s equation and dynamic programming but is unsure whether the required Markov assumptions hold. The document does not provide a solution, objective function details, or a response establishing that dynamic programming applies. Its useful contribution is the problem setup and the identification of key issues: how to define state, preserve the information needed for future decisions, and optimize a quantile-based evaluation rather than assume that a standard Markov formulation fits.

Key ideas

• The allocation problem consists of a sequence of discrete investment choices across multiple periods.
• A genetic algorithm has been used to search the strategy space, but the author seeks another optimization method.
• Strategies are scored using simulated fund-life quantiles compared with specified criteria.
• Dynamic programming depends on whether the state captures enough information to make future decisions well-defined.
• The document raises the applicability question but does not provide a method or solution.

Tags

# How would it be possible to use Dynamic Programming to search a space of investment strategies to find an optimum?


# How would it be possible to use Dynamic Programming to search a space of investment strategies to find an optimum?












As my question states, the problem I am having is finding a sensible way to search a large space. Any help or insight that could be provided would be hugely appreciated.

Currently I am trying to search through a space of possible investment strategies. This space has been restricted to 3 possible assets (Equity, Cash and Bonds) across 100 years where strategies are constant for 10 years at a time. I have also constrained the area by only allowing 100% investment in one asset or a 50/50 split between two. All of the fund must be invested at each time. This means that there are 10 times to choose between 6 possible combinations of investments. I have already preformed a basic search of the space using a labour intensive method of Genetic Algorithms which requires me to choose suitably optimal strategies across larger times, working my way down to decades starting at 50 year blocks. However I believe that there would be a better solution but my lack of knowledge in optimization is hindering me here. A strategy is ran through a programme to provide quantiles of a fund life which are then matched to given criteria.This is what indicates the suitability of a strategy.

I have been looking into using Bellman's equation but since it requires markovian assumptions I don't know if I can apply this. If anyone has any ideas that could be applied it would be a great help.

If anything I've said requires clarification or if I have been a bit vague on some information please let me know.

Thanks in advance.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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