2015年6月26日上午9:00-12:00，学术会堂702

学术报告（一）

主题：Some thoughts on market-consistent valuation

报告人：Jan Dhaene教授(比利时鲁汶大学，KU Leuven)

摘要：Insurance liabilities can often be expressed in terms of hedgeable (financial) and unhedgeable (actuarial) claims. Several recent insurance regulation frameworks require a market-consistent valuation of such liabilities and also of the related assets of the insurance company. The market-consistent valuation and pricing of such 'hybrid' liabilities is often not straightforward as it involves techniques from financial mathematics as well as from actuarial science. In case the claim can not be perfectly replicated, the market is incomplete and a unique market price of the claim is not readily available. Valuating based on actuarial judgement will have to be combined with observed market prices.

We investigate a framework for such a valuation of assets and liabilities related to an insurance policy or portfolio. In a first step of the valuation process, an best hedge for the liability is set up, based on the traded assets in the market, e.g. a mean-variance hedge. In a second step, the remaining part of the claim is valuation via a standard actuarial valuation principle. For a given choice of the optimal hedge and the actuarial valuation principle, this hybrid valuation results in a unique market consistent value.

*This is a joint work with Ben Stassen and Michel Vellekoop.

学术报告（二）

主题: How Robust is the VaR of Credit Risk Portfolios?

报告人：Jing Yao博士（布鲁塞尔自由大学，Vrije Universiteit Brussels）

摘要：In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, i.e., what is the maximum or minimum Value-at-Risk (VaR) that can be justified given a certain set of information? In the unconstrained homogeneous case, i.e., when the default probabilities, exposures and recovery rates of the different loans are known (and equal) but not their interdependence, some explicit sharp bounds are available in the literature. However, the problem is fairly more complicated when the portfolio is heterogeneous. In this regard, Puccetti and Rüschendorf (2012) and Embrechts et al. (2013) propose the rearrangement algorithm (RA) to approximate the unconstrained VaR bounds of a portfolio that can be heterogeneous. While their numerical examples provide evidence that the RA makes it indeed possible to approximate the sharp bounds accurately, their results also indicate that the gap between worst-case and best-case VaR numbers is typically very high. Hence, sharpening the VaR bounds by considering the presence of dependence information is of great practical relevance, but also hard to do because lack of sufficiently rich default data implies that knowledge of the joint default probabilities is typically not in reach. By contrast, the variance and perhaps also the skewness of the aggregated portfolio can be estimated statistically and can potentially be used as a source of dependence information allowing getting improvements of the VaR bounds.

We propose an efficient algorithm to approximate sharp VaR bounds in the unconstrained case, i.e., in comparison with the earlier algorithms that appeared in the literature, the algorithm that we propose is guaranteed to always converges to a candidate solution. Furthermore, we are able to adapt the algorithm so that it can deal with higher order constraints (variance, skewness, kurtosis...). A feature of our approach is that we are able to incorporate statistical uncertainty on the moment constraints. We apply the results to real world credit risk portfolios and we show that in all typical situations VaR assessments that are performed at high confidence levels (as in Solvency II and Basel III) are not robust and subject to significant model uncertainty.

Keywords:Bernoulli risks, Rearrangement algorithm, Moment bounds, Value-at-Risk.

* This is a joint work with Carole Bernard, Ludger Rüschendorf and Steven Vanduffel.

学术报告（三）

主题: A Fourier-Cosine Expansion Method for Fitting Loss Distributions and its Application

报告人：Xiao Wei副教授（中央财经大学中国精算研究院）

摘要：In this paper, we fit the probability density function to the sam- ple data by its Fourier-Cosine expansion, the parameters of the Fourier-Cosine expansion for the loss density function are estimated using the sample mean value estimator and the Schwarz’s Bayesian Information Criterion(BIC). Fit- ting tests of some common used distributions, such as the uniform distribution, the mixture of two Gamma distribution and the Pareto distribution, and the real loss data are provided to show the accuracy and the efficiency of the Fourier- Cosine expansion method. Applying this method to insurance, we derive the formula to calculate the risk measures of the loss data: Value at Risk (VaR), Conditional Tailed Expectation (CTE) of the loss will be computed. When ap- plying this method in options pricing in finance, it leads to a model free method for pricing the options.

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