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AIPlanner, AACalc, and Opal

The sources contained here comprise three asset allocation and consumption planning calculators based on mathematical principles, plus a SPIA pricing calculator.

AIPlanner uses deep reinforcement learning. It is computationally extremely demanding to train, but fast once trained.

AACalc attempts to shoehorn everything into Merton's portfolio problem. It is fast, and easy to use.

Opal is a research calculator that uses stochastic dynamic programming. It is complex, computationally demanding, and limited in terms of the scenarios it can handle.

The SPIA pricing calculator computes actuarially fair SPIA prices using up to date real, nominal, or corporate bond yield curves obtained from the U.S. Treasury.


Notable features of AIPlanner:

  • A heuristic approach that should deliver certainty equivalent performance that is within a few percent of the optimal solution.

  • The ability to train a single model for a variety of different scenarios.

  • Mortality handled probabilistically using mortality tables.

  • A GJR-GARCH model of stock volatility. Volatility of stock returns is partially predicatable, based on the prior period volatility.

  • A Shiller-esque model of stock prices. Stock prices may be over or undervalued, and mean revert to the random walk following fair price.

  • A Hull-White single factor bond model. Bonds have a yield curve, the yield curve evolves over time, and bond prices and returns reflect changes in the yield curve.

  • Gradual SPIA annuitization depending on age, wealth, and relative risk aversion.

  • Incorporation of the effects of standard error on the known values for stock and bond returns.

  • Taxation of assets based on an approximation to the U.S. tax code.

  • A web based API for strategy querying and evaluation.

  • A Monte-Carlo simulator to assess strategy performance.

  • An Angular web based front end.


Notable features of AACalc:

  • The closer the scenario is to Merton's portfolio problem, the more accurate the results.

  • A balance sheet approach - asset allocation can't be performed in isolation, but must be performed by taking into account the presence and size of Social Security, Pensions, 401(k)s, and income annuities.

  • Future contributions - the impact of any possible future contributions is handled by entering their expected annual amount, growth rate, and volatility.

  • Liability matching bonds - inflation indexed zero coupon bonds with a duration matching that of anticipated retirement cash flows are used as the risk free asset.

  • Income annuities - income annuities are a valuable tool in the retirement toolbox. This calculator optionally recommends the purchase of inflation indexed income annuities, that is single premium immediate annuities or deferred income annuities.

  • Admit what we don't know - returns from the stock market are unpredictable. We generate a range of results for different plausible scenarios.


Notable features of Opal:

  • Delivers, to within the limits of floating point calculations, the optimal solution for the simplified scenarios it is capable of handling.

  • Uses stochastic dynamic programming to compute optimal asset allocation and consumption strategies assuming time-wise independent returns.

  • A Monte-Carlo simulator to assess strategy performance.

  • A variety of correlation preserving bootstrapping and synthetic return generation options for the Monte Carlo simulator.

  • The ability to report the odds of portfolio failure, the time spent in the portfolio failure state, and certainty equivalent consumption metrics.

  • Optional handling of taxation in the Monte Carlo simulator using a variety of lot based accounting modules.

  • Mortality handled stochastically using mortality tables.

  • In addition to the standard asset classes, the ability to handle liability matching bonds, real annuities, and nominal annuities. Be warned though the annuity code often appears to invoke numerical instabilities.

  • When handling 3 or more asset classes the ability to speed up performance in exchange for some loss of optimality by using mean variance optimization thanks to the Systematic Investor Toolbox.

  • Graphical display of the optimal strategy and its performance thanks to GNUPLOT.

  • An optional deprecated web based front end to the program.

SPIA pricing calculator

Notable features of the SPIA pricing calculator:

  • Uses a variety of mortality tables.

  • Use of the current U.S. Treasury real and nominal yield curves, and the high quality markets corporate bond curve.

  • An optional web based front end.



  • AIPlanner is not Open Source, but is free for non-commercial use. Commercial use licenses are also available.

  • AACalc, Opal, and the SPIA pricing calculator have been released as Open Source. They are licensed under the GNU Affero GPL. Note, the Affero GPL requires that if you use the licensed code as part of a web service then you must release your code.

  • See the file LICENSE in the relevant sub-directories for further details.


  • Runs on Ubuntu 20.04 Linux and possibly other systems.

  • AIPlanner is written in Python, on top of Ray RLlib and PyTorch, with calls out to GNUPLOT.

  • The Opal backend is written in Java with call outs to R and GNUPLOT.

  • The AIPlanner web frontend is written in Angular. The remaining web frontends are written in Python using the Django framework.

  • The AIPlanner and Opal backends can be either run standalone, or in a server configuration talking to the frontend.

  • The AIPlanner and Opal backends perform minimal input sanity checking; responsibility for input sanity checking pushed on to frontend.

  • The Opal backend uses hill climbing to avoid exhaustive search of the solution space.

Getting started

  • It is suggested that Amazon EC2 be used for development work.

  • Obtain the sources:

    sudo apt install git
    git clone
  • If might do development work:

    cd aiplanner
    git config --global "<FirstName> <LastName>"
    git config --global "<>"
  • See ai/README for the Angular frontended Python based AIPlanner.

  • See web/README for the Django frontended Python based AACalc.

  • See opal/README for the Java based Opal.


AIPlanner is an machine learning based asset allocation and consumption planning calculator. Included are sources to two other similar calculators as well as a SPIA pricing calculator.




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