Applications of Monte Carlo Methods to Finance and Insurance

Monte Carlo methods are useful in solving a wide range of problems, both stochastic and deterministic, that cannot easily be solved using analytic methods. In this text, the authors describe a number of schemes for generating sequences of both pseudo-random and quasi-random numbers from a wide variety of probability distributions. They discuss several variance reduction methods aimed at improving the efficiency and the robustness of the simulation process. The text illustrates the practical application of such methods to real-life problems in finance and insurance by presenting several in-depth case studies, including a model for generating stochastic interest rates. It also addresses issues relating to the important concept of Value at Risk, a measure for assessing the risk and/or performance of assets and/or liabilities. It is thus an excellent source for continuing education involving solutions to new and unique actuarial problems. The authors take you through several examples that demonstrate how Monte Carlo methods can be used in a financial environment. Estimation of mortgage prepayments, the measurement of Value at Risk of a portfolio of assets and liabilities, and the calculation of the annuity payments from a reverse mortgage are included. From there the reader will be prepared to use Monte Carlo Methods to build model offices of insurance products, analyze the impact of alternative investment strategies, perform asset liability management, forecast the impact of natural catastrophes, and perform dynamic solvency testing.