Applications of Monte Carlo Methods to Finance and Insurance

algorithm antithetic variate appreciation rates approach approximately assume beta beta distribution binomial distribution bootstrap boundary values Chapter crude Monte Carlo denote density over 0,1 distribution function distribution over 0,1 employ Equation Example 5.1 exponential function over 0,1 Halton sequence Hammersley HECM Herzog hit-or-miss inequality in Step integral interest rate inversion method large number linear congruential low discrepancy sequences mean square error median Monte Carlo estimator Monte Carlo method mortgages negative binomial negative binomial distribution normal distribution normal random null hypothesis number of claims observations obtain output values p-value parameters percentile Poisson distribution portfolio probability density function probability distribution problem procedure pseudo-random numbers quasi-random numbers random numbers random variable Return to Step scheme Section set the initial simulated value standard deviation standard normal stochastic stratified sampling test statistic tion uniform distribution Value at Risk variance X₁