Qualified Pension Plans
and
Health Care for the Elderly
The Perfect Macroeconomic
Immunized Portfolio
Robert L. Brown
University of
Waterloo
ABSTRACT
Politicians, and the public, are beginning to worry about
how we will be able to afford the health care demands of an aging population
especially when the baby boom retires.
Politicians are also worried
about how much money is lost from tax revenues today because of the tax
advantages offered Employer-sponsored Qualified Pension Plans (QPPs) and Individual
Retirement Accounts (IRAs) including 401(k) plans. Under these schemes, contributions (for some plans, both
employer and employee) within limits are tax deductible and investment income
accrues tax free until the pension funds are taken as income. Thus, there is significant taxpayer
participation in these schemes.
While it is true that these
Qualified Plans are costing the government tax revenues today, it is also true
that the same schemes will create increased tax revenues for the government when
the baby boom retires and turns their pension assets into taxable retirement
income.
This paper models the extent of
the tax dollars being lost by the government today because of QPPs and IRAs,
but then goes on to project the extra revenue that will accrue to the
government from these same pension plans when the baby boom retires. It then points out that these extra
pension income dollars of tax revenue will come at exactly the time when the
baby boom will need extra government support to pay for their increased health
care delivery.
In short, we can create the
perfect macroeconomic immunized portfolio.
Application
of a Linear Regression Model to the Proactive Investment Strategy of a
Pension
Fund.
Kenneth G. Buffin PhD, FSA
Buffin Partners
Abstract: This paper presents
the methodology of a Linear Regression model applied to the analysis of the
risk-reward characteristics of a pension fund. It describes a set of seven
statistical measures of investment return and risk and demonstrates the
practical application of the model to a case study. The results highlight how
the analysis may be used to provide feedback and input to assist a proactive
investment strategy to achieve enhanced investment performance and reduced risk.
CLARA and the Selection of Representative Scenarios
Steve Craighead
Nationwide Financial
Corporate Actuarial
One Nationwide Plaza
1-27-01
Columbus, OH
43215-2220
Phone: 614-249-8775
Fax: 614-249-0725
Email:
craighs@nationwide.com
Web Page:
www.geocities.com/craighead_steven
Abstract: Kaufman and Rousseeuw in their 1990
work “Finding Groups in Data: An Introduction to Cluster Analysis”,
developed the algorithm CLARA (short for Clustering Large Applications). This algorithm is available in the
S-PLUS model environment and the public domain open source R language.
Using CLARA and some various
signal processing heuristics, we obtain 50 representative scenarios from a
total of 10,000 interest rate scenarios. Using representative scenarios, we
examine results from 106 data sets of multi-line corporate solvency
models. We observe representative
scenarios selected with CLARA perform very well across multiple years and
across multiple lines of business.
Multivariate Credibility for Aggregate Loss Models
by
Edward W. Frees
School of Business
975 University Avenue
University of Wisconsin-Madison
Madison, Wisconsin 53706
email: jfrees@bus.wisc.edu
Credibility
is a form of insurance pricing that is widely used, particularly in North
America. It is a special type of experience rating that employs a weighted
average of claims experience and a previously established price to determine a
new price, for each risk class under consideration. This article extends
traditional credibility formulas in two aspects. The new procedures are called
“multivariate credibility” because both aspects make use of
additional sources of data when compared to traditional formulas.
Specifically,
the first portion of the paper considers data from both the claims number and
claims amount processes. Assuming an aggregate loss model for total claims,
optimal insurance pricing formulas are derived. The insurance prices turn out
to be an intuitively appealing weighted average of the overall mean claim, the
claims number experience and the claims amount experience. The second portion
of the paper considers data from claims number and amount processes from
multiple lines of business. By using covariances among lines of business (that
are conditional on the unobserved heterogeneity), this article shows how to
derive more efficient insurance prices.
Accounting for covariance among different random quantities (securities) is standard practice in the investment industry. It is more difficult in an insurance context because of the heterogeneity associated with different risk classes. Nonetheless, ignoring this covariance has important ramifications, both theoretically and practically. For an illustrative sample of Massachusetts automobile claims, we show that the relative differences in accounting for and ignoring the covariance range from –3.9% to 14.5% for a selected bundle of insurance coverages.
Ratemaking
for Plan Reimbursement Provisions that Affect Severity in Health Insurance
Chuck Fuhrer
Most health insurance plans pay only a portion of the
loss suffered by the insured. These partial pay provisions have various names
such as deductibles, coinsurance, and copays. One of the principal reasons for
having these provisions is an attempt to limit the size of the loss by altering
the behavior of the insured. The insured is given a financial incentive to be a
more careful consumer of health care services and thus will select the most
cost-effective treatments. The
standard way of pricing these provisions is to build a size of claim
distribution in which the cost sharing provisions are ignored. Then, after
this, an arbitrary adjustment for the change in severity is applied. In this
paper, an alternative method is presented in which it is assumed that each
insured can express the utility of health improvement as a random function of
the amount of health care expense. The assumption is that the insureds will
then select the amount of healthcare expense that maximizes their utility.
Simulation
of Extreme Bivariate Values
R. Gonzalez
Abstract: Extreme
event risk is present in all areas of risk management and their accurate
modelling is of fundamental importance for practitioners. The class of possible
extreme distributions is identified explicitly by the extreme value theory and
in the one-dimensional case it contains only three distributions. This makes
applications of this theory relatively easy.
In the multivariate case, however, we not
only have to model the tails of distributions but also the dependence structure
of extreme events. This significantly complicates possible applications of the
theory and only recently the issue of efficient implementation has attracted
more attention.
In the paper, we study a method of simulation
of extreme bivariate values. It may be used to determine different risk
measure, like Value-at-Risk, expected shortfall or tail conditional
expectation. We consider several distributions characterized by different
specification of the copula.
"Some pricing
formulas of popular derivatives: an
approach with
released market assumptions"
Zhongxian Han
Mathematics Department
The Ohio State
University
Abstract will be
posted later.
Title Data Mining for Insurance Risk
Analysis
Author Zeng
Huang and Lijia Guo
Abstract
This study addresses issues and techniques for
insurance risk analysis using data mining algorithms, a new technology on the
horizon with great actuarial potential.
Data mining is a term applied to techniques that can be used to find
underlying structure and relationships in large amounts of data. With the recent advances of computer
technology, data mining is getting very popular for its successful applications
in many areas such as manufacturing (paper and sheet metal production control),
medicine (medical diagnosis and risk prediction), market research (mass mailing
and telemarketing), finance (financial time-series forecasting), and fraud
detection (credit-card fraud, income tax return fraud).
In this paper, we used data mining techniques to study
mortality risk factors. Instead of
using traditional parametric models, we used nonparametric models such as
neural network, binary decision tree, k nearest neighbors, and other. Using nonparametric models, we
explore arbitrarily complex relationships between mortality risk and the
underlying factors such as age, gender, amount exposures, participant status,
pat type and so on. Detailed discussions on data preprocessing, architecture
selecting, model training, model testing and model evaluating are presented in
the paper.
Abstract
Sales of equity-indexed annuities (EIAs) have rapidly increased since
the first offering in 1995, but the growth rates in sales have recently shown
signs of slowing because the current volatile equity market increases the costs
of guarantees in EIAs and hence decreases the participation rates. New EIAs need to be designed that are
similar to the existing ones such as point-to-point, annual reset and lookback
but have a cheaper guarantee and a higher participation rate. This paper proposes four types of EIAs
with higher participation rates: an up-and-in barrier EIA, an annual reset EIA
with up-and-in barriers, a partial-time lookback EIA, and a partial lookback
EIA with variable guarantee. It also presents explicit pricing formulas for
these EIAs by using Esscher transforms and discusses breakeven participation
rates.
Parametric Empirical Bayes Estimation of the Net Premium
wih Right Censored Data
Mostafa Mostayekhi
University of Nebraska-Lincoln
We consider an empirical Bayes estimation of the net
premium for one year policies, under a constant force of inerest with right
censored observations of times of claim causing events and constant claim
sizes.
Options on Mortality Contingent Claims
M.A. Milevsky and S.D. Promislow
York University
Consider a contract which gives the holder a right to purchase a life annuity at some future date at prices which are guaranteed now. Such provisions are typically found in U.S. variable annuity contracts. The problem of valuing such an option requires a different approach towards mortality measurement than the conventional actuarial technique. To model the uncertainty in future longevity, one must view the force of mortality as a stochastic process rather than a fixed function of time. In essence, we produce a type of “term structure” of mortality that is analogous to the traditional term structure of interest rates. It is shown that under certain natural assumptions both the mortality and the interest rate risk cn be hedged and the option to annuitize can be priced by finding a replicating portfolio involving life annuities, life insurance, and default free bonds.
<\p>
Quantile Hedging and Insurance Securitization
Diego Hernandez Rangel
Department of Statistics and Actuarial Science
Faculty of Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
The no arbitrage paradigm, as
presented by Harrison and Kreps (1979), is a powerful pricing approach under
relatively few assumptions. But in the context of incomplete markets we are left
with an interval of no arbitrage prices associated to an infinite set of
equivalent martingale measures (EMM). In consequence, several methods to select
an adequate EMM have been proposed. Risk minimizing strategies, Esscher pricing
and martingale approaches to premium calculation principles are just a few
examples.
Quantile hedging, a dynamic
version of VaR, is a methodology that allows calculating the probability of a
successful hedge given the initial investment in the replicating portfolio,
which is precisely the price calculated under the selected EMM. This
presentation discusses quantile hedging and some of its implications in
insurance securitization.
An XML based standard for representation of mortality
tables: How and Why?
Jacques Rioux Ph. D. , ASA
Associate Professor of Actuarial Science
College of Business and Public Administration
Drake University
Abstract: The Computer
Science section has mandated a small task force to propose a text based
standard for representation and exchange of mortality table data. I will
present the result of the task force's work and will provide examples of
applications of such a standard.
.
Generalized Faure Sequences
Ou Wang
Abstract: While Faure sequences are designed to have good uniformity property, it is know that its uniformity deteriorates as the dimensions increase. In this presentation, we propose a generalization of Faure sequences and study its efficiency by considering some finance applications.
Stochastic Analysis of Bonus Malus Systems
Shelley Zacks
Binghamton, New York
Benny Levikson
Haifa, Israel
Abstract: In a Bonus Malus system the annual premium is decreased if no claims are filed and the premium is raised if the insured files a claim. This method creates several levels, each having its own annual premiums. For each level we find the optimal cut off points of the damage levels of the insured where the insured is indifferent between filing and not filing claims. This is done for an infinite horizon using classical methods. The case of the finite horizon is solved using dynamic programming, where the cost to the insurer is analyzed and numerical examples are given.
