9:00 – 9:30 Antoine Soetewey
«Years of life lost applied to insurance contracts with finite horizon for cancer patients»
A B S T R A C T
Advancements in medicine and biostatistics have already resulted in a better access to insurance products for people diagnosed with cancer, in particular via the right to be forgotten which gives the right for an insurance applicant not to declare a previous cancer after a period of 10 years starting at the end of the therapeutic protocol. There is, however, still room for improvement in facilitating access to financial services for people with certain types of cancer. Over the last decade, the number of years of life lost (YLL) became a popular tool in biostatistics and epidemiology to measure differences in life expectancy or mortality, primarily thanks to its ease of interpretation and because information on the cause of death is not required. On the other hand, multistate models are a powerful statistical approach to study the evolution of individuals between different “states”, providing a convenient representation for life insurance contracts where benefits are associated to transition between states (Dickson et al., 2013; Pitacco, 2014). Based on 140,241 melanoma, thyroid and female breast cancer cases recorded by the Belgian Cancer Registry, we illustrate how cancer registry data can be used to fit a 3-state (healthy–cancer–death) multistate model to estimate YLL. We also show how the obtained results can be used to re-think the access of cancer patients to different insurance products, with a focus on financial contracts with a finite horizon such as loans and life annuities, by determining the financial burden to insurers derived from the loss of some years of life.

 

A B S T R A C T

The Rough Fractional Stochastic Volatility (RFSV) model of Gatheral et al. (2014) has led in the past few years to a shift of paradigm towards rough volatility models thanks to its ability to remarkably reproduce financial time series of past volatility as well as the observed implied volatility surface. Two tractable implementations have then been derived from this RFSV model with the rBergomi model of Bayer et al. (2016) and the rough Heston model of El Euch et al. (2018). We now show practically how to expand these two rough volatility models at larger time scales, we analyze their implications for the pricing of long-term life insurance contracts and we explain why they provide a more accurate fair value of such long-term contacts. In particular, we highlight and study the long-term properties of these two rough volatility models and compare them with standard stochastic volatility models such as the Heston and Bates models. For the rough Heston model, we manage to build a highly consistent calibration and pricing methodology based on a stable regime for the volatility at large maturity. This ensures a reasonable behavior of the model in the long run. Concerning the rBergomi model, we show that this model does not exhibit a realistic long-term volatility with extremely large swings at large time scales. We also show that this rBergomi model is not fast enough for calibration purposes, unlike the rough Heston model which is highly tractable. Compared to standard stochastic volatility models, the rough Heston hence provides efficiently a more accurate fair value of long-term life insurance contracts embedding path-dependent options while being highly consistent with historical and risk-neutral data.

 

A B S T R A C T

For the life cycle management of a vaccine and to leverage on existing historical data, GSK seeks to improve the statistical methods for clinical monitoring including both historical and new clinical trials data. The new methodology would involve complex multivariate statistical analyses to determine whether the results of a new clinical study are in line with historical data or if they are outliers. This is of particular interest in the scope of the post-marketing surveillance of immune response to a vaccine. In the context of a meta-analysis of vaccine clinical trials, a mixed effect model is fitted to the data to predict the antibody geometric mean titer. Based on a literature review, we selected three promising methods to detect whether a new study appears as an outlier in such meta-analysis with respect to the response variable: (1) the variance shift outlier model, (2) the external studentized residual and (3) the robust mixture model. In this poster, we present the results of a simulation study comparing these three methods to identify an outlier study in a meta-analysis of vaccine clinical trials.

 

A B S T R A C T

Survival analysis examines and models the time it takes for events to occur. The typical event is death, from which the name ‘survival analysis’ and much of its terminology derives. Since the data can only be collected over a finite period of time, the ‘time to event’ may not be observed for all the individuals. This is the case for example when a patient leaves a clinical study before it ends or she/he is still alive by the end of the study. In such a case, the death time (time to event) for this individual is unknown. Such a phenomenon, named censoring, creates some unusual difficulties in the analysis of survival data that cannot be handled properly by standard statistical methods. Most of the time, for the sake of simplification, ’independent censoring’ is assumed but in lot of cases that can lead to bias when there is actually ’dependent censoring’, that is when the survival time and the censoring time are stochastically dependent of each other. This occurs, e.g., when the event of interest is the time to death due to a certain disease, and censoring occurs (among other causes) when a patient dies due to another disease that has the same risk factors as the disease of interest. In traditional survival analysis, all subjects in the population are assumed to be susceptible to the event of interest, that is, every subject has either already experienced the event or will experience it in the future. However, in many situations it may happen that a fraction of individuals (long-term survivors) will never experience the event, that is, they are considered to be event free. For example, a treatment is assigned to patients in order to evaluate the effect on the recurrence of a disease. Many individuals never experience recurrences and thus can be regarded as cured or immune individuals. Models which deal with such data are called cure models. One popular of them, the mixture cure model, models the survival function by assuming that the underlying population is a mixture of two sub-populations: the sub-population of ‘susceptible’ (i.e. those who will experience the event and have finite survival time) and the sub-population of ‘nonsusceptibles’ (i.e. those who are event free and have an infinite survival time). In this presentation we will propose you a just developed fully parametric mixture cure model that allows dependent censoring thanks to the copulas. Our approach is inspired by a work of Claudia Czado and Ingrid Van Keilegom (2020).

 

A B S T R A C T

We investigate the valuation of annuity guarantees under a regime-switching model when the dynamics of the underlying stock price follows a self-exciting switching jump-diffusion process. In this framework, the intensity of shock arrivals, the return and volatility of shocks are modulated by a continuous-time hidden Markov chain with a finite number of states. The interest rate is stochastic and correlated to the stock market. In an incomplete market, we define an equivalent martingale measure to price a variable annuity contract with a minimum guarantee in case of death or life. Under this equivalent

martingale measure, we propose closed-form approximation formulas using the inverse Fourier transform technique. A numerical implementation highlights the impact of self-exciting jumps and economic regimes on the valuation of guarantees.

 

A B S T R A C T

Quantile regression (QR) is an alternative to the common mean regression. In QR, conditional quantiles of a response variable are estimated across values of predictors variables. When all data are fully observed, the regression coefficients are estimated by minimizing a check loss function. However, if the data are censored, minimizing the standard check loss function is no longer possible. As the beginning of a solution, it is possible to transform the minimization of the check function into a «maximum likelihood problem». Indeed, if we assume that the response variable conditional to the explanatory variables follows an Asymmetric Laplace distribution (ALD), it can be shown that minimizing the check function is equivalent to fit an ALD to the data. For censored data, fitting an ALD leads to inconsistent estimation of the regression coefficients. We propose to «Enrich» the Laplace Distribution by using Laguerre polynomial expansions. The idea behind this is to use the extra-flexibility provided by the Laguerre polynomials in order to better approximate the underlying distribution. Some finite samples simulations are presented in the case of interval-censored data. These demonstrate that using the Enriched Laplace Distribution leads to a better bias reduction than other existing estimating methods.