Bibliographic record
Abstract
In this thesis, we will introduce a consistent pricing method for Equity-Linked products and Equity-Indexed Annuities in particular. Due to their unique design, these products involve mortality and financial risks, and hence have to be valuated in an "incomplete market" framework. The no-arbitrage argument of Harrison and Pliska (1981) leads to the derivation of martingale probability measures for the valuation of these products. By assuming the separation of the insurance and annuity markets, we derive an age-dependent, mortality risk-adjusted martingale probability measure for term life insurance and pure endowment insurance. This method is similar to that of Jarrow and Turnbull (1995) and Ho and Lee (1986) in the sense that we derive martingale probability measures using the price information of standard insurance and annuity products exogenously. We then extend these martingale structures to include the financial market information. As a result, we are able to valuate an Equity-Linked product by pricing its death benefits and survival benefits separately. We also provide an alternative approach by considering the endowment insurance market and derive an associated age-dependent, mortality risk-adjusted martingale probability measure. In this case, an Equity-Linked product is valuated in a unified manner. Recursive pricing algorithms for equity-linked contracts that include surrender options are also introduced. The additional structure used to describe the dependence relationship defining the martingale measures are obtained using copulas. Numerical examples on EIAs are provided to illustrate the implementation of these methods. The aforementioned framework is developed under deterministic interest rates as well as under stochastic interest rates. The latter approach leads to martingale probabilities that evolve with the stochastic interest rates. Similar to Black, Derman and Toy, we assume that the volatilities for standard insurance and annuity prices are given exogenously. We then derive martingale probability measures allowing to value equity-linked products.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".