The increase of the expected lifetime, that is the longevity phenomenon, is accompanied by an increase of the number of seniors with a severe disability. Because of the significant costs of long term care facilities, it is important to analyze the time spent in long term care, as well as the...

This paper analyzes the risks in random sets and their implications for basket derivatives. Based on an extension of integration by parts for random set, we define stochastic dominance of order 1 and 2 for random sets. Since the ordering of sets, that is the inclusion, is a partial order, we...

We introduce Negative Binomial Autoregressive (NBAR) processes for (univariate and bivariate) count time series. The univariate NBAR process is defined jointly with an underlying intensity process, which is autoregressive gamma. The resulting count process is Markov, with negative binomial...

Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time....

We introduce new semi-parametric models for the analysis of rates and proportions, such as proportions of default, (expected) loss-given-default and credit conversion factor encountered in credit risk analysis. These models are especially convenient for stress test exercises. We show that...

We introduce a general state-space (or latent factor) model for time series and panel data. The state process has a polynomial expansion based dynamics that can approximate any Markov dynamics arbitrarily well, and has a latent, endogenous switching regime interpretation. The resulting...

The increase of the expected lifetime, that is the longevity phenomenon, is accompanied by an increase of the number of seniors with a severe loss of autonomy. Because of the significant costs of long-term care (LTC) facilities, it is important to analyze the time spent in LTC state, as well as...

The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile reproduction numbers observed in practice. We extend the...

Whereas data on return volatilities are available for a large number of assets, this is less frequently the case of covolatilities. We introduce an approach based on static and dynamic Wishart models to solve this problem of missing data. We first discuss the identification of the parameter of...

The ultra long run (ULR) discount rates are key inputs for valuing pension funds, life annuities, or firms with long run investments due to low carbon transition. However the corresponding zero-coupon bonds are only actively traded up to a last liquid point (LLP) such as 20 years, say. This...