Sujets de mémoire ACTU , D. Hainaut

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1 Sujets de mémoire ACTU , D. Hainaut May 3, 2018 Sex-specic mortality forecasting The objective of this master thesis is to test the eciency of the gender specic model for the joint mortality projection of several countries. The model, called 2-tier Augmented Common Factor model, extends the classical Lee and Carter and Li and Lee models, with a common time factor for the whole population, a sex specic period factor for males and females, and a specic time factor for each country within each gender. Reference: Sex-specic mortality forecasting for UK countries: a coherent approach. Ree Yongqing Chen, Pietro Millossovich. European Actuarial Journal (2017) 7: Comparison of Least square Monte Carlo and replicating portfolio for life insurance pricing. Solvency II requires insurers to calculate the 1-year value at risk of their balance sheet. This involves the valuation of the balance sheet in 1 year's time. As for insurance liabilities, closed-form solutions to their value are generally not available, insurers turn to estimation procedures. While pure Monte Carlo simulation set-ups are theoretically sound, they are often infeasible in practice. Therefore, approximation methods are exploited. Among these, least squares Monte Carlo (LSMC) and portfolio replication are prominent and widely applied in practice. The objective of this master thesis is to compare LSMC and RP, that are variants of regression-based Monte Carlo methods, they dier in one signicant aspect. While the replicating portfolio approach only contains an approximation error, which converges to zero in the limit, in LSMC a projection error is additionally present, which cannot be eliminated. Reference: the dierence between LSMC and replicating portfolio in insurance liability modeling. Antoon Pelsser, Janina Schweizer, Eur. Actuar. J. (2016) 6:

2 Gaussian Process Methods for Mortality Modelling The purpose of this thesis is to test Gaussian process regression and discuss how this method can be applied in forecasting mortality rates. We will follow the methodoly of Ruhao (2016) who introduce the new GPR model with weighted mean function and spectral mixture kernel. The GPR models will next be applied to mortality data and their performances are compared to the LC model. In the second part, we will combine the Gaussian process regression with a functional principal component analysis (MFPCA). The MFPCA model will next be applied to mortality data from Human Mortality Database. Reference: Gaussian Process and Functional Data Methods for Mortality Modelling. Ruhao Wu Phd Thesis University of Leceister Pricing of variable annuities with COS methods The purpose of this master thesis is to implement the Fourier-cosine method for pricing and hedging options. This method was developped by Fang and Oosterlee (2008) and applied by Alonso-Garcia (2017) for the pricing and hedging of variable annuities embedded with guaranteed minimum withdrawal benet (GMWB) riders. The COS method facilitates ecient computation of prices and hedge ratios of the GMWB riders when the underlying fund dynamics evolve under the inuence of the general class of Levy processes. The student will implement the COS method and compare this method with a classic Fourier Transform method. Reference: Pricing and hedging guaranteed minimum withdrawal benets under a general Levy framework using the COS method. Jennifer Alonso-Garcia Oliver Woody Jonathan Ziveyiz February 10, SSRN paper. A novel pricing method for european options based on Fourier-cosine series expansion. Fang, Oosterlee, SIAM J. Sci. Comput., (2), Rank-based methods for modeling dependence between loss triangles In this master thesis, the student will study ranks based methods for modeling depence between triangles. In order to determine the risk capital for their aggregate portfolio, property and casualty insurance companies must t a multivariate model to the loss triangle data relating to each of their lines of business. As an inadequate choice of dependence structure may have an undesirable eect on reserve estimation, a twostage inference strategy is proposed in the paper of Côté et al. (2016) to assist with model selection and validation. Generalized linear models are rst tted to the margins. Standardized residuals from these 2

3 models are then linked through a copula selected and validated using rank-based methods. Reference: Rank-based methods for modeling dependence between loss triangles Marie-Pier Cote, Christian Genest, Anas Abdallah, Eur. Actuar. J. (2016) 6: Pricing Interest Rate Derivatives with Model Risk The objective of this thesis is to study an interest rate derivative when there is the model risk in an interest rate model. We will consider a mean reverting interest rate process whose volatility process is not known. Most of prices of interest rate derivatives cannot be determined uniquely, based on this interest rate model. We study the price bounds of a derivative and propose how to calculate the price bounds by a trinomial model. Further we will analyze the model risk of derivatives and their portfolio numerically. Reference: Pricing interest rate derivatives with model risk, Satoshi Hosokawa and Koichi Matsumoto, J. Finan. Eng. 02, (2015) Market Consistent Valuation and Funding of Cash Balance Pensions Cash Balance (CB) pension plans became popular in the late 1990s, when a large number of Dened Benet (DB) pension plans converted to cash balance plans, taking advantage of the opportunity to transition to a plan that, apparently, mirrored a Dened Contribution (DC) arrangement, whilst staying in the dened benet category for regulatory purposes. Plan sponsors expected the CB plans to oer the same stable, predictable contribution rates as a DC plan, with the potential advantage of being cheaper than the equivalent DC plan. In this thesis, the student will analyze the CB pension and contributions using the methods and principles of nancial economics, to give a market consistent evaluation of the costs of the CB liability. Two interest rate models will be used for the valuation: the Hull&White and the G2++ models. Reference: Market-Consistent Valuation and Funding of Cash Balance Pensions North American Actuarial Journal Volume 18, Number 2, 2014 M. R. Hardy, D. Saunders & X. Zhu 3

4 Solvency II solvency capital requirement for life insurance companies based on expected shortfall This master thesis examines the consequences for a life annuity insurance company if the solvency II solvency capital requirements (SCR) are calibrated based on expected shortfall (ES) instead of value-at-risk (VaR). We will focus on the risk modules of the SCRs for the three risk classes equity risk, interest rate risk and longevity risk. The stress scenarios are determined using the calibration method proposed by EIOPA in We apply the stress-scenarios for these three risk classes to a ctitious life annuity insurance company. Reference: Solvency II solvency capital requirement for life insurance companies based on expected shortfall Tim J. Boonen. European Actuarial Journal (2017) 7: Variable annuity pricing with Time-Changed Lévy processes. The classic Black-Scholes option pricing model assumes that returns follow Brownian motion, but return processes dier from this benchmark in at least three important ways. First, asset prices jump, leading to non-normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. Timechanged Lévy processes can simultaneously address these three issues. The student will use this category of processes for pricing a variable annuity with a minimum guaranteed rate. Reference: Time-changed Levy processes and option pricing, Peter Carr, Liuren Wu, Journal of Financial Economics 71 (2004) Impact of volatility clustering on equity indexed annuities. Donatien Hainaut. Insurance: Mathematics and Economics 71 (2016) Estimation and Filtration of Time-changed Lévy Processes The objective of this work is rst to study Time-changed Lévy processes and to apply the Bates (RFS, 2006) or a MCMC methodology to the problem of estimating and ltering time-changed Lévy processes, using daily data on stock market excess returns over In contrast to density-based ltration approaches, the methodology recursively updates the associated conditional characteristic functions of the latent variables. We will examines how well timechanged Lévy specications capture stochastic volatility and the substantial outliers occasionally observed in stock market returns. 4

5 Reference: Estimation and Filtration of Time-changed Lévy Processes. David S. Bates Working paper, National Bureau of Economic Research. A MCMC Analysis of Time-Changed Levy Processes of Stock Return Dynamics HAITAO LI, MARTIN WELLS, and LONG YU Cont & Tankov: nancial modelling with jump processes. Chapman & Hall CRC nancial mathematics series Use of Hierarchical Clustering for analysis of time series. Financial time series display possibly the highest excess kurtosis and skewness of any asset class in capital markets. Capturing this requires a departure from classical modelling techniques. The premise is that stock prices jump and those jumps cluster. Initially, a model is proposed that is driven by a diusion and a Hawkes process to reproduce the clustering of shocks. The new element of the model is the use of hierarchical clustering to calibrate the distribution of the jumps. Partitioning the shocks identies shifts in the volatility regime of stock prices through time. This master thesis will be based on the work of Peter J. Zeitsch A Jump Model for Credit Default Swaps with Hierarchical Clustering. The paper is available on request. Boosting methods for neural networks. Boosting is a general method for improving the performance of learning algorithms A recently proposed boosting algorithm is AdaBoost It has been applied with great success to several benchmark machine learning problems using mainly decision trees as base classiers. In this master thesis we investigate whether AdaBoost also works as well with neural networks and we discuss the advantages and drawbacks of dierent versions of the AdaBoost algorithm. The dataset on which boosted neural networks is applied is a car insurance database. A reference paper is the work of Schwenk and Bengio, Boosting Neural Networks, to appear in neural computation. 5