Stochastic Programming Model for Asset and Liability Management using Network Flow Optimization
Publication Type:Conference Paper
Source:3rd Annual Business Complexity Conference, Center for Complexity in Business, Robert H. School of Business, University of Maryland, College Park, Maryland, USA. (2011)
Long Abstract This paper discusses an asset and liability management model formulated and solved as a stochastic linear programming (SLP) model. The stochastic network flow formulation (directed graph), an extension from Mulvey & Vladimirou (1991) and implemented by Ariyawansa and Felt (2004), uses nodes as assets and liabilities, and the arcs as fund flows (transactions). Three types of assets, i.e., equity, government securities, and bonds are considered, along-with annual contributions (liquid funds received and available that year for investment as well as disbursement), and annual payments (liabilities) for each year. The model uses a five year planning horizon. The starting year is deterministic, and is specified with initial values for nodes and arcs. For the later years, a discrete probability distribution with up-to four states is specified for each of the nine uncertain parameters of each period, namely, transaction costs, the annual return on each asset, annual contributions, and annual liabilities. The formulated SLP problem is written in the SMPS input file format (Gassmann & Schweitzer, 2001) to generate up-to 36^5 (~60 million) scenarios. It is currently possible to solve a "sub-problem" of the above using IBM ILOG CPLEX Optimization Suite (IBM Corp., 1987, 2009). Thus, the paper develops a five-year fund-flow (sources and uses of funds) plan for the Pension Fund Sector. The computational burden involved clearly suggests use of parallelization along-with decomposition methods. The model is scalable and, in its present formulation, would be of an order of 36^n scenarios to solve a problem with an n-year planning horizon. The current AUM of Employee Provident Fund Organization is approximately Rs. 300,000 Crores (pension fund plus provident fund), about 66 Billion USD. The 57 th Annual Report of EPFO (2009-10) is used to generate input data for the problem. The problem assumes that funds are initially invested equally in all three asset classes, and then an optimal five-year fund management plan has been derived. The results suggest an investment plan where assets are created first in equity, then government securities and bonds in that order.
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