We explore generalizations of the pari-mutuel model (PMM), a formalization of an intuitive way of assessing an upper probability from a precise one. We discuss a naive extension of the PMM considered in insurance, compare the PMM with a related model, the Total Variation Model, and generalize the natural extension of the PMM introduced by P. Walley and other pertained formulae. The results are ...

In the Lee-Carter framework, future survival probabilities are random variables with an intricate distribution function. In large homogeneous portfolios of life annuities, Value-at-Risk or Conditional Tail Expectation of the total yearly payout of the company are approximately equal to the corresponding quantities involving random survival probabilities. This paper aims to derive some bounds in...

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach co...

The implementation of appropriate statistical techniques for monitoring conditional VaR models, i.e, backtesting, reported by institutions is fundamental to determine their exposure to market risk. Backtesting techniques are important since the severity of the departures of the VaR model from market results determine the penalties imposed for inadequate VaR models. In this paper we make six con...

Recent crises in the financial industry have shown weaknesses in the modeling of Risk-Weighted Assets (RWAs). Relatively minor model changes may lead to substantial changes in the RWA numbers. Similar problems are encountered in the Value-at-Risk (VaR)-aggregation of risks. In this article, we highlight some of the underlying issues, both methodologically, as well as through examples. In partic...

Modeling high-dimensional dependence is widely studied to explore deep relations in multiple variables particularly useful for financial risk assessment. Very often, strong restrictions are applied on a dependence structure by existing high-dimensional dependence models. These restrictions disabled the detection of sophisticated structures such as asymmetry, upper and lower tail dependence betw...

We discuss the CreditRisk+ methodology from the perspective of the moment generating function of the credit factors. This representation lends itself to a new recursion formula for the portfolio loss distribution that is more accurate and considerably faster, particularly for large portfolios. We discuss how the model can be extended to incorporate correlations between risk factors and derive t...

Maximum Relative Drawdown measures the largest percentage drop of the price process on a given time interval. More recently, Maximum Relative Drawdown has become more popular as an alternative measure of risk. In contrast to the Value at Risk measure, it captures the path property of the price process. In this article, we propose a partial differential equation approach to determine the theoret...

The traditional Value at Risk (VaR) is a very popular tool measuring market risk, but it does not incorporate liquidity risk. This paper proposes an extended VaR model to integrate liquidity risk for intraday trading strategies using high frequency order book data. We estimate the one step ahead liquidity adjusted intraday VaR called(LAIVaR) for both bid and ask positions, considering several t...