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Theses

Numerical methods for the ALM

Adel Cherchali 1, 2 
2 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
Abstract : This thesis deals with the modeling and the construction of efficient numerical methodsfor the Asset and Liability Management (ALM) in insurance. The first part of thisthesis introduces a synthetic ALM model that catches the key features of life insurancecontracts. This model keeps track of both market and book values to apply theregulatory profit sharing rule. Second, it introduces a determination of the creditingrate to policyholders that is close to practice and is a trade-off between the regulatoryrate, a competitor rate and the available profits. Third, it considers an investment inbonds that enables to match a part of the cash outflow due to surrenders, while avoidingto store the trading history. We use this model to evaluate the Solvency CapitalRequirement (SCR) with the standard formula. The second part copes with efficientnumerical methods to compute the SCR. More specifically, we study the MultilevelMonte-Carlo (MLMC) method developed by Giles [Gil08] to estimate the expectationof a maximum of conditional expectations. This problem arises naturally when consideringmany stress tests and appears in the calculation of the interest rate moduleof the standard formula for the SCR. We obtain theoretical convergence results thatcomplements the recent work of Giles and Goda [GG19] and gives some additionaltractability through a parameter that somehow describes regularity properties aroundthe maximum. We then apply the MLMC estimator to the calculation of the SCRat future dates with the standard formula using the model developed in the first part.Last, we compare it with estimators obtained with Least Square Monte-Carlo or NeuralNetworks and show the relevance of the MLMC method in this context.
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Adel Cherchali. Numerical methods for the ALM. General Mathematics [math.GM]. Université Paris-Est, 2021. English. ⟨NNT : 2021PESC1102⟩. ⟨tel-03606038⟩

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