Cumulative Prospect Theory in Intertemporal Portfolio Optimization
Summary
The document presents a portfolio optimization problem with cumulative prospect theory (CPT) preferences over a multi-period horizon. The questioner highlights reference dependence and probability weighting as reasons the objective may be non-time-separable and time-inconsistent, making a standard Bellman recursion appear unsuitable. They ask for an example implementation or a more scalable method, particularly for a VBA or spreadsheet setting.
The only approach described is brute-force enumeration on a binomial tree: evaluate feasible allocation paths, calculate conditional probabilities and CPT utility, then select the path with the highest utility. The author reports that this becomes impractical as the number of time steps grows, with spreadsheet storage also becoming a constraint. No solution, code, numerical results, or formal treatment of how to handle time inconsistency is provided. The post records a modeling and computational challenge rather than establishing a general algorithm; any proposed optimization method would need to specify how the agent revises decisions and how the CPT objective is evaluated across paths.
Key ideas
- The question concerns portfolio choice over multiple periods under cumulative prospect theory preferences.
- Reference dependence and probability weighting are identified as sources of time nonseparability and inconsistency.
- The proposed brute-force method evaluates feasible allocation paths on a binomial tree and compares CPT utility.
- The author reports that path enumeration and spreadsheet capacity limit the approach as the horizon grows.
- The document requests guidance but does not provide a scalable algorithm or demonstrate a solution.
Tags
Full text
# Dynamic portfolio optimization with cumulative prospect theory # Dynamic portfolio optimization with cumulative prospect theory i'm new to this forum and i hope i can get some help or at least some guidance how to tackle the following problem: I'm tasked to write a VBA Macro that conducts an intertemporal portfolio optimization with prospect theory preferences. As far as i already understand, CPT (cumulative prospect theory) isn't time-separable due to the reference dependence (static ref. point, not dynamic adjusting) and moreover, not time-consistent due to the decision weights. This means i have to write some sort of forward algorithm to recalculate the new path of portfolio allocations for each timestep until the end of my investment horizon. It also means the economic agent revises her/his strategy at any point in time and thus the usual Bellman approach cannot be used. I tried to understand the problem using an intertemp. Lagrange optimization just to get a feeling for the Euler Equations and i guess 'm running into some computational issues...but thats not my question, however, any hints are appreciated here. well..What i have tried is this: So far i simulated for a binomial tree each possible strategy, calculated conditional probabilities for those strategies, that are feasible, calculated the CPT utility and picked the path/allocation with the highest CPT. I know this is some stupid brute force approach and there are surely more clever ways to handle this. Moreover, this problem gets really complex once i exceed five timesteps (and my Excel refuses to go on as i reach my storage limit after seven steps). My question is, whether sthere is some sort of example-VBA code or excel sheet that demonstrates this dynamic programming / intertemporal portfolio optimization problem where the solutions cannot be simply obtained by Bellman. Any hints whether i'm on the right track is highly appreciated. All best
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.