The maximum entropy method was originally proposed as a variational technique to determine probability densities from the knowledge of a few expected values. The applications of the method beyond its original role in statistical physics are manifold. An interesting feature of the method is its...

We present some results of the application of maximum entropy methods to determine the probability density of compound random variables. This problem is very important in the banking and insurance business, but also appears in system reliability and in operations research. The mathematical tool...

One of the main problems in the advanced measurement approach to determine operational risk regulatory capital, consists of the computation of the distribution of losses when the data is made up of aggregated losses caused by different types of risk events in different business lines. A similar...

The problem of determining probability densities from data is important in many fields, in particular in insurance and risk analysis. The method of maximum entropy has proven to be a powerful tool to determine probability densities from a few values of its Laplace transform. This is so, even...

A risk manager may be faced with the following problem: she/he has obtained loss data collected during a year, but the data only contains the total number events and the total loss for that year. She/he suspects that there are different sources of risk, each occurring with a different frequency,...

An important problem in the insurance and banking industries is that of pricing risk or premium valuation. When the empirical data is not large, and loss distributions are inferred from the data, a potentially large sample dependence of the premia on the data is to be expected. The maximum...

In risk management the estimation of the distribution of random sums or collective models from historical data is not a trivial problem. This is due to problems related with scarcity of the data, asymmetries and heavy tails that makes difficult a good fit of the data to the most frequent...

Diversification practices by banks affect their own risk of failing and the risk of the banking system as a whole (systemic risk). A seminal theoretical work has shown that linear diversification can reduce the risk of a bank failing, but at the cost of increasing systemic risk. Later, a...

One of the controversies of diversification is that it may not be beneficial to banks, as it tends to increase systemic risk. Recent theoretical and empirical work have addressed this problem. We argue, from a theoretical perspective, that this controversy ultimately depends on how risk is...

Here we present an application of two maxentropic procedures to determine the probability density distribution of compound sums of random variables, using only a finite number of empirically determined fractional moments. The two methods are the Standard method of Maximum Entropy (SME), and the...