Actuarial applications of the linear hazard transform

In this thesis, we study the linear hazard (LH) transform and its applications in actuarial science. Under the LH transform, the survival function of a risk is distorted, which provides a safety margin for pricing insurance products. Combining the assumption of alpha-approximation, the net single premium of a continuous insurance policy can be approximated in terms of the net single premiums of discrete insurance ones. We also find that the LH transform is good at fitting by regression between two mortality curves. With the method of mortality fitting, the mortalities for the future years can be predicted as well. Finally, the applications of the LH transform for an insurance company's asset managements, such as mortality swap, risk ordering and optimal reinsurance, are explored.