A CHANCE CONSTRAINED PROGRAMMING APPROACH TO PENSION PLAN MANAGEMENT WHEN ASSET RETURNS ARE HEAVY TAILED

Patrick L. Brockett
University of Texas at Austin

Abstract

 The objective of providing retirement income is important for workers and employers.
This paper show how to define a model to trade off the various investment goals, tax
deductibility considerations and contribution factors involved when an employer is
choosing how to fund a defined benefit plan.  Every employee wants more retirement
income, and most employers would like to use as little money as possible in order to
provide the best possible pension plan. The employer's goal involves many uncertain
factors, such as the life expectancy of employees for ages after retirement; the
pension funds; returns on investments which will accrue to money markets, stocks or
bonds and the rates of the changes in cost of living, salaries and inflation. How to
optimally decide on contribution levels necessary in order to satisfy the employer's
conflicting goals is a complicated problem.  The existence of uncertainty (randomness)
in critical decision variables causes further complications in the analysis. A usual
actuarial method for handling uncertainty is to use deterministic approaches based on
expected values. When the funding falls below or above this point estimate, however,
this can necessitate expensive remedial funding actions to preserve favored tax status
for contributions and to avoid tax penalties. Here we present a policy-making (chance
constrained programming) model for pension plan funding which openly represents the
uncertainty.  While in unusual circumstances, the policy will have to be modified at
the end of the year to retain qualification; the frequency with which this occurs is
(unlike using expected values) controllable by the actuary.  With this technique the
actuary can explicitly trade off the costs associated with remedial actions, tax
penalties, etc. with the investment returns in order to meet the pension plan goals.
Significant factors in the uncertainty associated with pension funding include the
return on financial instruments in the capital markets, and these return distributions
have been found empirically to follow heavy tailed (e.g., extreme value, or stable law)
distributions.  Accordingly, the chance constraints in our model will utilize heavy
tailed distributions for computations.

This is joint work with Jean Ai, Georgios Chimonides, and Li Sun