Markowitz principles for multi-period portfolio selection problems with moments of any order
Bibliographic record
Abstract
The multi-period portfolio selection problem is formulated as a Markowitz mean–variance optimization problem in terms of time-varying means, covariances and higher-order and intertemporal moments of the asset prices. The crux lies in expressing the number of shares of any particular asset to be transacted on any future trading date, which is a non-anticipative process, as a polynomial of the changes in the discounted prices of all the risky assets. This results in the expected return of the portfolio being dependent on not only the means of the asset prices, but also the higher-order and intertemporal moments, and its variance being dependent on not only the second-order moments, but also the higher-order and intertemporal moments. As illustrations, we study the portfolio selection problems including the discrete version of the Merton problem. It is shown numerically that the efficient frontier obtained from Markowitz's discrete multi-period formulation coincides with that from Merton's continuous-time formulation when the number of rebalancing periods is ‘large’. The effects of dynamic trading, in particular volatility pumping, in comparison with a static single-period model are measured by a non-dimensional number, Dyn( P ) ( P , number of trading periods), which quantifies the relative gain due to dynamic trading. It is sufficient to rebalance the portfolio a few times in order to get more than 95% of the gain due to continuous trading.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".