Equity-linked products

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In this research project, I will develop a stochastic structure for insurance liabilities. This new structure relies on the modelling of future liabilities instead of martingale mortality probabilities. In this setup, the underlying short-term rate follows the Ho and Lee model. The insurance liability structure should have similar assumptions to those of Ho and Lee for interest rate models, for instance constant volatility and non-constant martingale probabilities. Once the interest rate and insurance structures are defined, we can extend the martingale measure to include the index process (we employ the Cox, Ross and Rubinstein model for the stock index). I will use common-shock models, hierarchal models as well as copulas to extend the martingale measure and be able to valuate equity-linked products. I plan to conduct an empirical study on insurance products valuated using arbitrage-free theory. The goal is to identify the mortality loadings implied by standard insurance premiums and find actuarial premium principles that fit the observed martingale mortality probabilities. Similar to dynamic reinsurance markets, I also plan to investigate different hedging strategies (mean-variance hedging, efficient hedging (quantile hedging), super-replication, etc.) considering that insurance companies selling equity-linked contracts can invest in a reinsurance portfolio. Using various risk measures including the well-known Value at Risk and Conditional Tail Expectation, I will also analyze the effect of the different trading strategies on the profit-risk ratio.