Optimal Investment for Retail Company in Electricity Market
Bibliographic record
Abstract
Considering an optimal investment problem for a retailer in electricity market, the objective is to seek the optimal investment decision that maximizes the weighted sum of the expected return and the variance of wealth. Unlike existing works, the price fluctuation of both the wholesale and retail side of electricity market is considered, and the retailer can invest its wealth in electricity market and traditional financial market simultaneously. Hence, there is a complicated wealth dynamic, which is the main challenge in our work. In this paper, by utilizing the method of Lagrange multiplier and the classical Tchebycheff inequality, we first show that the investment problem is a quadratic programming problem in terms of the decision variable, and thus has a unique optimal solution. Then, a closed-form optimal solution is derived by solving the stationary equation and comparing the feasible solution interval. Based on the optimal solution, we find the key price, which will affect the investment is the wholesale price rather than the retail price. Moreover, with a similar analysis approach, we also provide the optimal solution considering a more general model, which allows the retailer to purchase the electricity temporarily to avoid the supply shortage. Extensive simulations demonstrate the better performance of the proposed solution over the Kelly strategy widely used in the financial market.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".