Minimum Relative Entropy Inference for Normal and Monte Carlo Distributions

Inference is ubiquitous in financial applications: stress-testing and scenario analysis, such as in[Mina and Xiao, 2001], explore the consequences of specific market scenarios on the distribution of the portfolio loss. Similar, portfolio construction techniques such as [Black and Litterman, 1990] inject views on specific factor returns into the estimated distribution of a broad market. A general approach to perform inference under partial information based on the principle of minimum relative entropy (MRE) was explored in [Meucci, 2010]. In the original paper, the general theory was supported by two applications: an analytical solution under normality, and a numerical algorithm for distributions represented by scenarios, such as Monte Carlo, historical, or categorical. Here we enhance both the analytical and the numerical implementations of [Meucci, 2010] drawing from results in [Colasante, 2019]. In Section 2 we state well-known results to set the notation and background.