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August 29-30, 2011
Workshop on “Actuarial and Financial Statistics” Satellite
The International Statistical Institute (ISI) World Statistics Congress,
recurring every two years and being among the main activities of the ISI, takes
place in Dublin, Ireland, on 21-26 August, 2011. Following the 2011 ISI World
Statistics Congress, EURANDOM organizes a EURANDOM-ISI Satellite Workshop. This
workshop will be concerned with statistics, focusing on insurance and financial
applications. a. Statistics of Lévy processes in insurance and finance 1. The high dimensionality of the problems under consideration often forces analysts to rely on Monte Carlo simulation methods of which the reliability is not always guaranteed, in particular not in a risk management setting. 2. The adopted models are often too simplistic, and do, for example, not quickly incorporate the arrival of market information, nor do they incorporate sophisticated dependence structures between the risks. Furthermore, the effect of model risk is often not taken into account. 3.The risk measures under consideration are often specified in terms of high quantiles the estimation of which may rely on extreme value theory. But a treatment which is based on extreme value theory may perform at its own extremes when the central part of the data is entirely ignored, or when second order properties are not taken into account. 4. Economic modeling in many cases suffers from the non-observability of the basic ingredients and results are in many cases highly sensitive to the adopted filtering, instrumental variables, or substitution approach. This is true for example in interest rate modeling. 5. While Lévy processes have been generally accepted to provide useful
models, their statistical treatment is still in its infancy, especially in a
high-dimensional setting.
Registration (is closed) Registration is obligatory for all participants (organizers and speakers too!). Registration fee is 75 euros, to be paid by all
participants (excluding organizers and speakers).
Monday August 29
There will be a poster presentation during the breaks Tuesday August 30
Katrien Antonio (University of Amsterdam) Micro-level stochastic loss reserving for general insurance To meet future liabilities general insurance companies will set–up reserves. Predicting future cash–flows is essential in this process. Actuarial loss reserving methods will help them to do this in a sound way. The last decennium a vast literature about stochastic loss reserving for the general insurance business has been developed. Apart from few exceptions, all of these papers are based on data aggregated in run–off triangles. However, such an aggregate data set is a summary of an underlying, much more detailed data base that is available to the insurance company. We refer to this data set at individual claim level as ‘micro–level data’. We investigate whether the use of such micro–level claim data can improve the reserving process. A realistic micro–level data set on liability claims (material and injury) froma European insurance company is modeled. Stochastic processes are specified for the various aspects involved in the development of a claim: the time of occurrence, the delay between occurrence and the time of reporting to the company, the occurrence of payments and their size and the final settlement of the claim. These processes are calibrated to the historical individual data of the portfolio and used for the projection of future claims. Through an out–of–sample prediction exercise we show that the micro–level approach provides the actuary with detailed and valuable reserve calculations. A comparison with results from traditional actuarial reserving techniques is included. For our case–study reserve calculations based on the micro–level model are to be preferred; compared to traditional methods, they reflect real outcomes in a more realistic way. Umut Can (EURANDOM and University of Tilburg) Goodness of Fit Testing with Empirical Copulas Copulas are increasingly used in finance and actuarial sciences to model multivariate dependence. A fundamental question in this respect is the goodness-of-fit of a specified parametric family of copulas for a given sample of multivariate observations. We propose a sequential scanning innovation operation to transform the empirical copula process asymptotically into a standard Wiener process. This transformation paves the way to the development of a variety of asymptotically distribution-free goodness-of-fit tests for copula-based models. Florence Guillaume (Eurandom) Multivariate Asset Pricing Models: Some Extensions of the αVG Model We propose a class of multivariate Lévy and Sato models for option pricing built upon a Lévy or Sato time change Brownian motion where the time change consists of a weighted sum of an idiosyncratic and a common component. We consider the particular case of Gamma subordinators and we distinguish in between a reduced model where the asset logreturn margins are of Variance Gamma (VG) type and a generalized model where the margins remain Lévy or Sato-distributed but not necessarily VG distributed anymore. These models can be seen as an extension of the αVG model proposed by Semeraro [1] where the VG margins are replaced by more flexible distributions. We calibrate the different models for a period ranging from June 2008 until October 2009 including therefore the recent credit crisis period. In particular, we show that the reduced models usually fail to reproduce the market correlations when calibrated by using the decoupling calibration procedure whereas the generalized models can adequately reproduce the market implied correlations when a penalty term which assesses the correlation goodness of fit is included into the calibration surface optimizer. Moreover, the proposed Sato models are able to fit univariate option surfaces quotes both for low and high volatility regime periods and consequently outperform both the multivariate Black-Scholes model and the proposed multivariate Lévy models. [1] Semeraro, P. (2008). A multivariate Variance Gamma model for financial applications. International Journal of Theoretical and Applied Finance, 11, 1-18. Chris Klaassen (University of Amsterdam) Semiparametric Estimation Theory for Discretely Observed
L'evy Processes For discretely observed Lévy
processes we have to deal with data with an infinitely divisible distribution.
We show that for every such distribution the corresponding location family is
complete. As a consequence it can be proved that the semiparametric statistical
model for our data is nonparametric, in fact. Andrea Krajina (University of Göttingen) Modeling Jump Dependence using Lévy
Copulas Roger Laeven (University of Tilburg) Model Uncertainty and Robustness: A Dual Theory for Decision under Risk and Ambiguity This paper
axiomatizes a new theory for decision under risk and ambiguity. Our theory is
dual to the theory of variational preferences, introduced by Maccheroni,
Marinacci and Rustichini (2006). As a special case, we obtain a preference
axiomatization of a decision theory that is dual to the popular maxmin expected
utility theory of Gilboa and Schmeidler (1989). In addition, we discuss the
possibility of resolving paradoxes that appear in other decision theories and
characterize risk and ambiguity aversion within our new theory. Sara Maccaferri (KU Leuven) Lévy processes and the financial crisis: can we design a more effective deposit protection? Lévy processes have been
applied in various financial settings to overcome the main shortcomings of the
Gaussian distribution, since they allow for fat tails and jumps. In the present
paper we propose to use Lévy processes to simulate the distribution of losses
deriving from bank failures. The application of Lévy processes is expected to
provide successful results to this aim since bank failures are unexpected, rare
events. Kees Oosterlee (CWI) Efficient valuation methods for contracts in finance and insurance In this presentation we will discuss the use of Fourier cosine
expansions for pricing financial and insurance derivative contracts. Mitja Stadje Robust Portfolio Choice
Michele Vanmaele (University of Ghent) Föllmer-Schweizer or Galtchouck-Kunita-Watanabe decomposition? A comparison and description. The relationship between the Föllmer-Schweizer (FS) decomposition and the Galtchouk–Kunita–Watanabe decomposition will be elaborated under the minimal martingale measure. The difference between these two decompositions is highlighted in a very practical example, and the martingale tools that enhance this difference are illustrated in the semimartingale framework as well. The FS-decomposition will be described using the predictable characteristics. Emiliano Valdez (University of Connecticut) Longitudinal Modeling of Insurance Claim Counts Modeling insurance claim counts is a critical component in the ratemaking process for property and casualty insurance. This article considers using copulas to model the number of insurance claims in a longitudinal context. To address the limitations of copulas in the case of discrete data, we adopt a "jittering" method for the claim counts. Elliptical copulas are proposed to accommodate the intertemporal dependency of the "jittered" claim counts, and thus the subject-specific heterogeneity on the frequency of claims. The resulting predictive distribution and the corresponding credibility of claim frequency are derived for ratemaking purposes. For empirical illustration, we analyze an unbalanced longitudinal dataset of claim counts in automobile insurance from a major insurer in Singapore. We demonstrate that the copula with "jittering" method outperforms several standard count regression models in the prediction. Tim Verdonck (KU Leuven) Bibliography Dacheng Xiu (University of Chicago, Booth School of Business) Dissecting and Deciphering European Option Prices using Closed-Form Series Expansion We seek a closed-form series approximation of European option prices under a variety of diffusion models. The proposed convergent series are derived using either the Hermite polynomial approach or the undetermined coefficients method. Departing from the usual option pricing routine in the literature, our model assumptions are fairly general, with no requirements for affine dynamics or explicit characteristic functions. Moreover, the closed-form expansions provide a distinct insight into how and on which order the model parameters affect option prices, in particular for close-to-maturity options. Such explicit formulae are advantageous over alternative numerical solutions of partial differential equations or simulation methods in regard to real-time calibration and hedging with contingent claims. With closed-form expansions, we explicitly translate model features into option prices, such as stochastic interest rate, mean-reverting drift, and self-exciting or skewed jumps. Numerical examples illustrate the accuracy of this approach.
Links to former workshops on Lévy processes: 1. Applications of Lévy Processes in
Financial Mathematics; EURANDOM, Eindhoven, The Netherlands, June 22 - 23,
2001 3. Credit Risk under Lévy Models; ICMS, Edinburgh, The United Kingdom, September 19 - 21, 2006
Conference Location
For all information on how to come to Eindhoven, please check http://www.eurandom.tue.nl/contact.htm
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Last updated
23-09-11,
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