Programme YRD 28/09/2018

09h00 : Gilles Mordant

09h30 : Alexandre Jacquemain

10h00 : Pr Eugen Pircalabelu (replacing Nathalie Lucas)

10h30 : Coffee break
 
11h00 : Antoine Soetewey

11h30 : John John Ketelbuters

12h00 : Fadoua Zeddouk
 
12h30  : sandwich lunch in the cafeteria

Abstracts

Gilles Mordant
"Distribution comparison tests based on self-similar transport of measure"

Abstract :
In statistics, and especially in nonparametric statistics, having natural order is crucial. It is however well known that ranks do not canonically exist in R^d.
In this talk, we show a new method relying on measure transportation onto one dimension using self-similar objects helping to easily perform multivariate distribution comparison tests. We show that our testing procedures are computationally effective and have nice connections with existing tests. In addition to finite sample performance and properties, we provide simulation results. Next, we consider an extension to the study of independence tests. This is based on a distance measure which involves Sklar’s theorem and the general idea developed for comparison tests.”

Alexandre Jacquemain
"Lorenz regression"

Abstract :
We lay out a regression procedure based on the Lorenz curve, a tool famous for its use in economics to describe income inequalities. The methodology is semiparametric in the sense that a monotone link function is assumed between the dependent variable and a linear index involving explanatory variables. Yet, no further assumption is made on the exact nature of that link. In that sense, our framework runs in the same lines as the single-index model proposed by Ichimura [1993]. In applications, we argue that our methodology selects the covariates weights which reproduce as much as possible the observed inequalities in the dependent variable. If all covariates are continuous, we show that the obtained estimator is a special case of the monotone rank estimator proposed by Cavanagh and Sherman [1998]. In presence of discrete covariates, a continuity correction is developed. We present a goodness-of-fit measure, which refers to the proportion of explained inequality. Since the maximization program appears hard to tackle with usual methods, we present a genetic algorithm to solve it. Finally, we assess the performance of our estimator compared to Ichimura’s nonlinear least-squares through a series of Monte-Carlo simulations.

Nathalie Lucas
"Actuarial models for health and disability insurance"

Abstract :
The main purpose of the research is to develop i) efficient actuarial models of pricing and reserving and ii) risk classification techniques for health insurance products.
Whereas classical approach treats health insurance using life techniques, we aim to better study health claims randomness and integrate longevity and other systematic risks (i.e. inflation) in the analysis. The special dependence between morbidity and mortality will be emphasized.
The last section will introduce dynamic heterogeneity in health claims using a Hidden Markov Model (HMM).

Antoine Soetewey
"Life and Health Actuarial Pricing: a Biostatistics Approach"

Abstract :
It is generally thought that patients having suffered from a cancer have a lower probability of survival compared to healthy people. Due to this aggravated risk and the relatively small number of patients wishing to take out insurance coverage in case of death, the insurance industry is reluctant to grant such a guarantee. However, survival and life expectancy of cancer patients have been increasing over the last decades and we can reasonably assume that they will keep increasing in the future thanks to medical and technological progress. In regard to this, France passed a law referred as "the right to forget", that is, the right for a person subscribing to a contract not to declare a previous cancer after a period of 10 years after the end of the therapeutic protocol (Sapin and Touraine, 2017). This period being reduced to 5 years if the person is a minor. But some questions remain: The thresholds of 10 and 5 years are arbitrary and does not reflect survival of the persons having suffered from a cancer. There remains some ambiguity about what is considered as treatment, so what marks the end of a therapeutic protocol and in the end when the patient will start to benefit from this right? Finally, this right is very binary and not flexible at all.
 
The aim of the thesis is twofold: (i) To develop a method to adequately estimate the threshold after which cancer patients can be considered as cured, and (ii) to find a proper way to adapt the actuarial pricing of life insurance products to each category of risk, disease, person, etc. The goal is also to demonstrate that for some types of cancer, the survivors actually have a chance of survival comparable to that of the general population, or pose a moderately increased risk and could therefore be covered in the event of death. This involves measuring and quantifying the potential excess mortality so that the premiums claimed reflect the risk in terms of financial services.

John John Ketelbuters
"Time consistent actuarial valuation of credit risk"

Abstract :
A common actuarial pricing method consists to sum up the expected loss and a risk margin. Time-consistent valuation methods satisfy by definition the tower property of expectations. This feature is highly desirable because it is equivalent to stating that a risk that will be almost surely cheaper than another one at a future date should already be cheaper today. However this property is breached if we add a risk margin to the expected cost of future claims. Based on the work of Pelsser and Ghalehjooghi (2016),  we adapt actuarial valuation techniques for computing time-consistent prices of credit insurance products. We show that time-consistent prices are solutions of a partial differential equation that we solve numerically.

Fadoua Zeddouk
"Pricing of longevity derivatives and cost of capital"

Abstract :
The significant improvement in longevity in most developed countries increases the annuity providers’ exposure to longevity risk. In order to hedge this risk, new longevity derivatives have been proposed (longevity bonds, q-forwards, survivor swaps, options...). Although academic researchers, policy makers and practitioners have talked about it for years, the longevity-linked derivatives available in the financial market are still limited due to the pricing difficulty. In this paper, we compare different existing pricing methods and propose a Cost of Capital approach following Levantesi and Menzietti (2017) framework. Our method is designed to be more consistent with Solvency 2 requirement i.e. the Solvency Capital Required should cover with 99.5% probability the unexpected losses on a one-year time horizon. The price of longevity risk is determined for a S-forward and a S-swap but can be used to price other longevity-linked securities. The Hull & White and CIR extended models are used to represent the evolution of mortality over time. We use data for Belgian population to derive prices for the proposed longevity linked securities based on the different methods.