PDF Ebook Asset-Liability Management Modelling with Risk Control by Stochastic Dominance
An Asset-Liability Management model with a novel strategy for controlling risk of under-funding 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 measure (and control) risk of underfunding. A small numerical example is provided to demonstrate advantages of this new model which includes stochastic dominance constraints over the basic model.
Adding stochastic dominance constraints comes with a price. It 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. A structure exploiting interior point method is applied to this problem. A specialized interior point solver OOPS can deal efficiently with such problems and outperforms the industrial strength commercial solver CPLEX. Computational results on medium scale problems with sizes reaching about one million of 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.
The Asset-Liability Management (ALM) problem has crucial importance to pension funds, insurance companies and banks where business involves large amount of liquidity. Indeed, the financial institutions apply ALM to guarantee their liabilities while pursuing profit. The liabilities may take different forms: pensions paid to the members of the scheme in a pension fund, savers’ deposits paid back in a bank, or benefits paid to insurees in the insurance company. A common feature of these problems is the uncertainty of liabilities and the resulting risk of underfunding. The other major uncertainty originates from asset returns. Together they constitute a nontrivial difficulty in how to manage risk in the model applied by the financial institution. The need for multi-period planning additionally complicates the problem.
A paradigm of stochastic programming [1, 22] is well-suited to tackle these problems and has already been applied in this context as shown in [33] and in many references therein. One of the first industrially applied models of this type was the stochastic linear program with simple recourse developed by Kusy and Ziemba in [24]. This model captured certain characteristics of ALM problems: it maximized revenues for the bank in the objective under legal, policy, liquidity, cash flow and budget constraints to make sure that deposit liability is met as much as possible. Under computational limits at the time when it was developed, this model took the advantage of stochastic linear programming so as to be practical even for the large problems faced in banks. It was shown to be superior compared to a sequential decision theoretical model in terms of maximizing both the initial profit and the mean profit. However, the risk management was not considered in this work; only expected penalties of constraints violation were taken into account.
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PDF Ebook Asset-Liability Management Modelling with Risk Control by Stochastic Dominance
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