Optimal execution under jump models for uncertain price impact
Bibliographic record
Abstract
ABSTRACT In the execution cost problem, an investor wants to minimize the total expected cost and risk in the execution of a portfolio of risky assets in order to achieve desired positions. A major source of the execution cost is the price impact of both the investor's own trades and other concurrent institutional trades. Indeed, the price impact of large trades has been considered to be of the main reasons for fat tails of the short-term return's probability distribution function. However, current models in the literature on the execution cost problem typically assume normal distributions. This assumption fails to capture the characteristics of tail distributions due to institutional trades. In this paper we argue that compound jump-diffusion processes naturally model uncertain price impacts of other large trades. This jump diffusion model includes two compound Poisson processes where random jump amplitudes capture uncertain permanent price impacts of other large buy and sell trades. Using stochastic dynamic programming, we derive analytical solutions for minimizing the expected execution cost under discrete jump-diffusion models. Our results indicate that, when the expected market price change is nonzero, likely due to large trades, assumptions on the market price model and values of mean and covariance of the market price change can have a significant impact on the optimal execution strategy. Using simulations, we computationally illustrate minimum CVaR execution strategies under different models. Furthermore, we analyze qualitative and quantitative differences of the expected execution cost and risk between optimal execution strategies, determined under a multiplicative jump-diffusion model and an additive jump-diffusion model.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
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".