X. Yang, J. Gondzio, A. Grothey,
Abstract
An Asset-Liability Management model with a novel strategy
for controlling the risk of underfunding is presented in this paper.
The basic model involves multiperiod decisions (portfolio
rebalancing) and deals with the usual uncertainty of investment
returns and future liabilities. Therefore it is well-suited to a
stochastic programming approach. A stochastic dominance concept is
applied to control risk of underfunding through modelling chance
constraint. A small numerical example and an out-of-sample backtest
are provided to demonstrate advantages of this new model which
includes stochastic dominance constraints over the basic model and a
passive investment strategy.
Adding stochastic dominance constraints comes with a price. This
complicates the structure of the underlying stochastic program.
Indeed, new constraints create a link between variables associated
with different scenarios of the same time stage. This destroys the
usual tree-structure of the constraint matrix in the stochastic
program and prevents the application of standard stochastic
programming approaches such as (nested) Benders decomposition and
progressive hedging. Instead we apply structure-exploiting interior
point method to this problem. The specialized interior point solver
OOPS can deal efficiently with such problems and outperforms the
industrial strength commercial solver CPLEX on our test problem set.
Computational results on medium scale problems with sizes reaching
about one million variables demonstrate the efficiency of the
specialized solution technique. The solution time for these
nontrivial asset liability models seems to grow sublinearly with the
key parameters of the model such as the number of assets and the
number of realizations of the benchmark portfolio, and this makes
the method applicable to truly large scale problems.
Key words: Asset/Liability Management, Stochastic Programming, Risk Control, Stochastic Dominance Constraints, Interior Point Methods.