Thesis title : Statistical inference for extreme risk measures: Implication for the insurance of natural disasters

Fig.1: Price and yield distribution of wheat and wine growing.
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THESIS OBJECTIVES

Contribute to the development of new statistical methods to model French farm income in order to study its insurability. Extreme value theory, Bayesian statistics and copulas are the three theoretical pillars on which my thesis is based.

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RISK MANAGEMENT AND APPROPRIATE INSURANCE COVERAGE.

In recent decades, extreme weather events related to natural disasters and market deregulation have impacted agricultural production and income. Price volatility, increased by the globalization of trade in raw materials, and climate change are affecting the volume and quality of production, thus jeopardizing the survival of farms. Protection against climate and market risks fall within a good risk management and thus farmers’ insurance coverage. 

THREE APPROACHES

The modelling of the dependency structure between the agricultural risks, using the statistical tool of copulas. Next, an overview related to the possibility of establishing farm income insurance is proposed.  
The second contribution is the proposition of a new approach, called Extreme-PLS, for dimension reduction adapted to distribution tails. The objective is to find linear combinations of predictors that best explain the extreme values of the response variable in a regression context.  
Since the applicability of extreme value methods is limited to large sample sizes, the scarcity of extreme events limits the availablility of data, my third contribution extends to Bayesian statistical methods. The main interest is to study how the introduction of prior information on the data can improve the estimation of extreme risk measures on small samples.  

Finally, to face extreme events related to agricultural risks, we aim at adapting some financial instruments to cover the risk provided that they provide emergency financing and compensate farmers.


Fig. Price/yield correlations and wheat productions by region in France (Low correlations are in light pink)
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PUBLICATIONS

1. M. Bousebata, G. Enjolras & S. Girard, Extreme Partial Least-Squares regression, submitted, 2021. https://hal.inria.fr/hal-03165399/document
2. M. Bousebata, G. Enjolras & S. Girard. The dependence structure between yields and prices: A copula-based model of French farm income, Agricultural and Applied Economics Association (AAEA), 2020. https://hal.inria.fr/hal-02933766/document

International conferences
1. M. Bousebata, G. Enjolras & S. Girard. The dependence structure between yields and prices: A copula-based model of French farm income, European Association of Agricultural Economists (EAAE), July 2021, Prague, Czech Republic.
2. M. Bousebata, G. Enjolras & S. Girard. Extreme Partial Least-Squares regression, Extreme Value Analysis (EVA), Jun 2021, Edinburgh, UK. [Video]
3. M. Bousebata, G. Enjolras & S. Girard. The dependence structure between yields and prices: A copula-based model of French farm income, Annual Meeting of the Agricultural and Applied Economics Association (AAEA), August 2020, Kansas City, USA.
4. M. Bousebata, G. Enjolras & S. Girard. Bayesian estimation of natural extreme risk measures, Application to agricultural insurance, 10th conference of the international society for Integrated Disaster Risk Management (IDRiM), Oct.2019, Nice, France.

National conferences
1. M. Bousebata, G. Enjolras & S. Girard. Extreme Partial Least-Squares regression, 52èmes Journées de Statistique de la SFdS, 2020, Nice, France.
2. M. Bousebata, G. Enjolras & S. Girard,Bayesian estimation of natural extreme risk measures, Application to agricultural insurance, Global Challenges Science Week: International interdisciplinary days of Grenoble Alpes, June 2019, Grenoble, France.
3. M. Bousebata, G. Enjolras & S. Girard. Estimation bayésienne des mesures des risques naturels extrêmes. Application à l'assurance du risque agricole, Assises Nationales des Risques Naturels, March 2019, Montpellier, France.