Related papers: Using Monte Carlo Methods for Retirement Simulatio…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
What grounds the rule of thumb that a(n American) retiree can safely withdraw 4% of their initial retirement wealth in their first year of retirement, then increase that rate of consumption with inflation? I address that question with a…
A group of approaches for calculating forensic likelihood ratios first calculates scores which quantify the degree of difference or the degree of similarity between pairs of samples, then converts those scores to likelihood ratios. In order…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…
Monte Carlo Approaches for calculating Value-at-Risk (VaR) are powerful tools widely used by financial risk managers across the globe. However, they are time consuming and sometimes inaccurate. In this paper, a fast and accurate Monte Carlo…
Metamodels, or the regression analysis of Monte Carlo simulation results, provide a powerful tool to summarize simulation findings. However, an underutilized approach is the multilevel metamodel (MLMM) that accounts for the dependent data…
Monte Carlo methods are now an essential part of the statistician's toolbox, to the point of being more familiar to graduate students than the measure theoretic notions upon which they are based! We recall in this note some of the advances…
We construct the maximally predictable portfolio (MPP) of stocks using machine learning. Solving for the optimal constrained weights in the multi-asset MPP gives portfolios with a high monthly coefficient of determination, given the sample…
Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the…
A scientometric analysis of Monte Carlo simulation and Monte Carlo codes has been performed over a set of representative scholarly journals related to radiation physics. The results of this study are reported and discussed. They document…
The gradual accumulation of damage and dysregulation during the aging of living organisms can be quantified. Even so, the aging process is complex and has multiple interacting physiological scales -- from the molecular to cellular to whole…
We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. The model learns the features necessary for an…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
Hedging methods to mitigate the exposure of variable annuity products to market risks require the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means these sensitivities…
In the context of life insurance with profit participation, the future discretionary benefits ($FDB$), which are a central item for Solvency~II reporting, are generally calculated by computationally expensive Monte Carlo algorithms. We…
Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient…
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…