Optimal Investment, Consumption and Life Insurance Problem with Stochastic Environments
Bibliographic record
Abstract
Optimal investment, consumption and life insurance problem with stochastic environments for a CRRA wage-earner is solved in this study.  The wage-earner invests in the financial market with one risk-free security, one risky security, receives labor income and has a life insurance policy in the insurance market. A life insurance policy is purchased to hedge the financial wealth for the beneficiary in case of wage earner premature death. The interest rate and the volatility are stochastic. The stochastic interest rate dynamics of risk-free security follow a Ho-Lee model and the risky security follow Heston’s model with stochastic volatility parameter dynamics following a Cox-Ingersoll-Ross (CIR) model. The objective of the wage-earner is to allocate wealth between risky security and risk-free security but also buy a life insurance policy during the investment period to maximize the expected discounted utilities derived from consumption, legacy and terminal wealth over an uncertain lifetime. By applying Bellman's optimality principle, the associated HJB PDE for the value function is established. The power utility function is employed for our analysis to obtain the value function and optimal policies. Finally, numerical examples and simulations are provided.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".