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精算通讯第六卷第一期
2007 上海香港---保险精算论坛会议内容
时间：2007 年 8 月 18 至 19 日
地点：华东师范大学理科大楼 A 座 504 多功能厅
Speech 1：Economic Capital and Regulation of
Banks and Insurers
Speaker:
Harry Panjer ， Department of Statistics
and Actuarial Science，University of Waterloo
Abstract
In many countries, insurers and banks are separately
regulated. In some countries, banks and insurers are not
allowed to be part of the same conglomerate and share
capital. This raises questions about the efficient use of
capital and return on equity to shareholders. In this
empirical study we view economic capital from a
solvency perspective with the focus on downside risk.
The key question addressed is “What efficiencies, if any,
are gained by allowing banks and insurers of different
types to merge an thus share capital” We examine to
what degree bank and insure performance have been
correlated historically, especially in the downside tail.
This case study is based on a selection of banks, life
insurers and property-casualty insurers.
Speech 2：The Compound Poisson Surplus Model with
Interest and Liquid Reserve
Speaker: Jun Cai ， Department of Statistics and
Actuarial Science, University of Waterloo (A joint work
with Runhuan Feng and Gordon E. Willmot)
Abstract
We modify the classical compound Poisson surplus
model by including liquid reserve and interest on an
insurer’s surplus. When the surplus is below a fixed
level called liquid reserve limit, it is kept as liquid
assets, which do not earn interest. As soon as the
surplus attains the limit, the surplus in excess of the
limit gains interest at a constant rate. The modified
model is consistent with the classical compound
Poisson risk model if the limit goes to infinity. And it
reduces to the compound Poisson risk model with
interest when the limit is set to be zero. We shall study
ruin probability and other ruin-related quantities in the
modified compound Poisson surplus model by means of
the Gerber-Shiu function and discuss the impact of
interest and liquid reserve on the ruin probability, the
deficit at ruin, and other ruin quantities. First, we derive
a system of integro-differential equations for the
Gerber-Shiu function. By solving the system of
equations, we obtain the general solution to the
Gerber-Shiu function based on the Volterra equations of
the second kind and defective renewal equations. Then,
we give the exact solutions for the Gerber-Shiu
function when the initial surplus is equal to the liquid
reserve level or equal to zero. These solutions are the
key to the exact solution for the Gerber-Shiu function in
general cases. Moreover, exact solutions to the
Gerber-Shiu function are derived respectively when the
discount rate is zero and claim sizes follow exponential
and Erlang-2 distributions.
Speech 3：On the Consistence of Credibility Premiums
regarding Esscher Principle
Speaker:
Xianyi Wu，Department of Statistics and
Actuarial Science, East China Normal University (A
joint work with Maolin Pan and Rongming Wang)
Abstract
In this paper, we investigate the problems of
convergence
of
experience-based
ratemakings
regarding the Esscher principle. In addition to the
Bayes and the classical credibility premiums, we
suggest a new credibility formula for the Esscher
premium. Then we show the convergence of the Bayes
and the newly defined credibility premiums towards the
individual premium and point out that the classical
credibility premium does not generally converge to the
individual premium by presenting a sufficient and
necessary condition under which the classical
credibility Esscher premium converges to the individual
premium. A simulation study is carried out to illustrate
the theoretical conclusions.
Speech 4：Discussions on Embedded Value
Speaker: Lo Won How ， China Pacific Insurance
(Group) Co., LTD
Abstract
This presentation on “Discussions on Embedded Value”
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covers 1) What is Embedded Value (EV), how to
calculate EV, the purpose of using it, who’s using it and
the recent development. 2) An example of EV
calculation for a simplified bundled product is
introduced with all the major assumptions used and the
EV movement analysis is also provided. 3) The
considerations of using EV in China.
Speech 5：Stress Testing for Life Insurance Companies
Speaker: Estella Chiu ， Regional Chief Actuary,
HSBC Insurance (Asia Pacific) Holdings Ltd.
Abstract
1. Why is stress testing needed
- to quantify the risk of extreme but plausible events
- to evaluate capital adequacy under these scenarios
2. Selection of Scenarios
- prescribed vs non-prescribed
- short term vs medium term
- economic vs non-economic
- ripple effects
- special considerations for PAR plans
3. Role of the Actuary
- selection of scenarios
- performing the test
- recommendation and management action
- presentation to the Board
4. A few examples
5. Stress test and Risk based capital
Speech 6：Risk Models in a Markovian Environment
Speaker:
Yi Lu ， Department of Statistics and
Actuarial Science, Simon Fraser University
Abstract
We consider risk processes with the property that the
intensity rate of the Poisson arrival process and the
distribution of the claim sizes vary in time depending
on the state of an underlying (external) Markov jump
process. The main feature of the model is the flexibility
on modeling the arrival process in the sense those
periods with very frequent arrivals and periods with
very few arrivals may alternate, and that the states of
the Markov jump process could describe, for example,
epidemics types in health insurance or weather
conditions in car insurance. In this talk I will present
our recent work in risk theory for the model, which
includes the results on the expected discounted penalty
functions and their decompositions, moments of the
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dividend payments and other related problems. Main
approaches to obtain these results will be discussed and
numerical illustrations will also be given.
Speech 7：Pricing Participating Products Under a
Generalized Jump-Diffusion with a Markov-switching
Compensator
Speaker: Hailiang Yang，Department of Statistics
and Actuarial Science, The University of Hong Kong
(A joint work with Ken Siu and John Lau)
Abstract
We propose a model for valuing participating life
insurance products under a generalized jump-diffusion
model with a Markov-switching compensator. We
suppose that the jump component is specified by the
class of Markov-modulated kernel-biased completely
random measures. Our model provides additional
flexibility to incorporate the impact of structural
changes in macro-economic conditions and business
cycles on the valuation of participating policies by
introducing a continuous-time Markov chain. In
particular, we assume that the market interest rates, the
drift, the volatility and the compensator of the reference
asset switch over time according to the state of the
Markov chain. We employ the Esscher transform to
determine an equivalent martingale measure under the
incomplete market setting. We shall conduct simulation
experiments to compare the fair values of participating
products implied by our model with those obtained
from other existing models in the literature and
highlight some features that can be obtained from our
model.
Speech 8：On the Classical Risk Model with Interest
and Dividend Payments
Speaker: Kam Chuen Yuen, Department of Statistics
and Actuarial Science, The University of Hong Kong
Abstract
In this talk, we consider the classical risk model with
interest and dividend payments. We first study the
classical risk model with interest and a constant
dividend barrier. Under constant interest, we derive
an integro-differential equation for the Gerber-Shiu
expected discounted penalty function. We obtain the
solution to the integro-differential equation which is in
the form of an infinite series. In some special cases with
exponential claims, we are able to find closed-form
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expressions for the Gerber-Shiu expected discounted
penalty
function.
Finally,
we
extend
the
integro-differential equation to the case that the surplus
is invested in an investment portfolio with stochastic
return on investments. We next examine the classical
risk model with constant interest under the threshold
strategy. In this set-up, we investigate the expected
discounted dividend payments and the Gerber-Shiu
expected discounted penalty function. We also derive
closed-form expressions for these functions in the case
of exponential claims.
Speech 9：On the Tail Behavior of a Random Difference
Equation with Sub-exponential Innovations
Speaker: Qihe Tang，Department of Statistics and
Actuarial Science, The University of Iowa
Abstract
Consider a random difference equation described as
that R is equal in distribution to X+YR, where X, Y,
and R are independent random variables. A challenging
problem is to find the distribution of R knowing the
distributions of X and Y. In this talk we focus on this
problem and discuss the tail behavior of R. Applications
to actuarial science are proposed.
Speech 10：The Lee-Carter Model for Forecasting
Mortality, Revisited
Speaker: Siu-Hang Li, Department of Statistics and
Actuarial Science, The University of Waterloo;
Wai-Sum Chan, Department of Finance, Chinese
University of Hong Kong
Abstract
Interrupting phenomena are commonly encountered in
time-series data analysis with the study of mortality
trends being no exception. Nevertheless, previous
demographic forecasts have paid little attention to the
existence of such phenomena. In this study we use
mortality data from Canada and the United States to
perform time-series outlier analysis on the key
component of the Lee-Carter model: the mortality index.
We begin by employing a systematic outlier detection
process to ascertain the timing, magnitude, and
persistence of any outliers present in historical trends of
the mortality index. We then try to match the identified
outliers with important events that could possibly
justify the vacillations in human mortality levels. At the
same time, we adjust the effect of the outliers for model
精算通讯第六卷第一期
re-estimation. The empirical results indicate that the
outlier-adjusted model could achieve better fits and
more efficient forecasts of variables such as the central
rates of death and the life expectancies at birth. Finally,
we conclude our study with possible extensions on the
valuations of life annuities and the probabilistic
distribution of the highest attained age, incorporating
the effect of mortality improvement portrayed by the
revised model.
Speech 11：Reforming Chinese Healthcare through
Public-private Partnership
Speaker:
Wil Chong, Head of Life & Health,
Swiss Reinsurance Company Beijing Branch
Abstract
This presentation looks at an efficient and viable model
for health financing in China. We review the global
development of medical insurance from the perspective
of national healthcare financing. The extraordinary
growth of the Chinese health insurance market is also
scrutinized. Through surveys and active discussion with
insurance companies and health and social security
officials both at the policy and local levels, we identify
the opportunities and challenges if China wishes to
advance its health protection system. Our research
findings have been validated with the industry and
experts in this field. A high-level future vision is also
offered for policymakers’ consideration.
Speech 12：Determine the Required Solvency Capital
Requirement for P&C Insurers in China Market
Speaker:
Xie Zhigang, Shanghai University of
Finance & Economics (SUFE)
Abstract
The purpose of this study is to analyze the regulatory
solvency capital requirement related to the solvency
risks of P&C insurers in China market. The core issue
is to decide reserving and underwriting risk factors,
based on the specific market structure, available data
records and a series of assumptions for the P&C
insurers. The results of calculation are implemented to
several sample P&C companies and compared to the
current standards of calculating solvency margin.
Finally the study provides recommendations for
establishing a risk-oriented approach of solvency
supervision and capital requirement model for P&C in
China market.
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