Portfolio replication and least squares Monte Carlo with application to insurance risk management

The Solvency II framework requires insurers to market-consistently value their own funds. The task is challenging given that insurance liabilities are typically not traded financial instruments and closed-form solutions are mostly not available. One solution is to obtain an estimate of the future value of liabilities through pure Monte Carlo simulations, which, however, in risk-capital calculations quickly becomes too time-intensive. This thesis deals with Least Squares Monte Carlo (LSMC) approaches, Regress-Now and Regress-Later, that yield an approximation to the value of the insurance liabilities. The asymptotic properties of the methods are analyzed. It is shown that the Replicating Portfolio technique commonly applied by insurers, corresponds to LSMC with Regress-Later. Thereby a theoretical foundation for the Replicating Portfolio technique is provided. Lastly, advantages and disadvantages of Replicating Portfolio and LSMC (with Regress-Now) are discussed.