Bibliographic record
Abstract
Publisher Summary This chapter is a survey of the theoretical results and practical uses of the capital growth approach. It presents the alternative formulations for capital growth models in discrete and continuous time. Various criteria for performance and requirements for feasibility are related in an expected utility framework. Typically, there is a trade-off between growth and security with a fraction invested in an optimal growth portfolio determined by the risk aversion criteria. Models for calculating the optimal fractional Kelly investment with alternative performance criteria are formulated. In capital accumulation under uncertainty, a decision maker must determine how much capital to invest in riskless and risky investment opportunities over time. The investment strategy yields a steam of capital, with investment decisions made so that the dynamic distribution of wealth has desirable properties. The distribution of accumulated capital to a fixed point in time and the distribution of the first passage time to a fixed level of accumulated capital are variables controlled by the investment decisions. An investment strategy which has many attractive and some not attractive properties is the optimal strategy, where the expected logarithm of wealth is maximized. This strategy is also referred to as the Kelly strategy. It maximizes the rate of growth of accumulated capital asymptotically. With the Kelly strategy, the first passage time to arbitrary large wealth targets is minimized, and the probability of reaching those targets is maximized. However, the strategy is very aggressive since the Arrow-Prat risk aversion index is essentially zero. Hence, the changes of losing a substantial portion of wealth are very high, particularly if the estimates of the returns distribution are in error. In the time domain, the chances are high that the first passage to subsistence wealth occurs before achieving the established wealth goals
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.014 | 0.003 |
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".