Integration and Approximation in High Dimensions – a Tutorial

Often they are high-dimensional expected values: Example: In 1995 Traub and Paskov computed values of ‘mortgage-backed obligations’. In the USA people buying a house borrow money from a bank. In return, the bank holds a ’mortgage’. US mortgages last for 30 years, and may be repaid at the end of any month, making 30 × 12 = 360 repayment possibilities. The monthly change in the interest rate is treated as a random variable, with some assumed (usually Gaussian) probability distribution. There are 360 random variables, so the computed quantity is a 360-dimensional expected value. (The success of that experiment, using “quasi-Monte Carlo methods”, generated much interest in quasi-Monte Methods.)