• ISSN: 2010-023X
    • Frequency: Bimonthly
    • DOI: 10.18178/IJTEF
    • Editor-in-Chief: Prof.Tung-Zong (Donald) Chang
    • Executive Editor: Ms. Cherry L. Chen
    • Abstracting/ Indexing: Engineering & Technology Digital Library, ProQuest, Crossref, Electronic Journals Library, DOAJ , EBSCO, and Ulrich's Periodicals Directory
    • E-mail: ijtef@ejournal.net
IJTEF 2010 Vol.1(3): 247-253 ISSN: 2010-023X
DOI: 10.7763/IJTEF.2010.V1.45

Application of Fuzzy Mathematical Model in Assets-Liabilities

Manoj Kumar Jain, A. K. Dalela, and Sandeep Kumar Tiwari

Abstract—The literature on fuzzy logic treats it very much as a new concept, distinct from that of probability logic, even though both ascribe to event numbers in interval [0, 1]. An individual financial planning is a decision problem faced by an individual whose aim is to manage his consumption and investment decisions to achieve a real set of financial targets given by his current and expected income, over a long term horizon. Various financial systems in the corporate as well as individual context are under pinned by a cash flow balancing movement. A basic aspect of financial planning encompasses such matching behavior of cash flows and is given by the generic label-Asset and Liability Management (ALM). From a mathematical perspective above models can be set up in an educational form involving non-negative variables which represent inflow and outflow of funds and put back of retained assets and funds from one planning period to the next planning period [1, 5, and 7]. ALM has emerged as an ideal framework to address this type of decision problem under uncertainty, in which the achievement of a strategic objective is made conditional on the effective management of assets and liabilities over time. The individual problem can be regarded as an extension of a personal savings consumption model with a limited number of savings opportunities and a rich set of individual and regulatory constraints with a long-term objective. The peculiarity of the individual ALM problem comes from the extent and implications of a modeling approach, in which, principle is expected to capture the different features of the management of a financial position with a typically long-term horizon, up to and sometimes beyond retirement for an investor whose preferences may very well change over the planning horizon [1, 9]. An ALM model for controlling risk of underfunding is presented in this paper. The basic model involves multi period decisions (portfolio rebalancing) and deals with the usual uncertainty of investment returns and future liabilities for pensioner. Therefore it is well-suited to a fuzzy programming approach. A fuzzy programming dominance concept is applied to measure (and control) risk of underfunding of pension Asset and Liability.

Index Terms—PV-Present Value ALM – Asset- liability Management

[1]School of Studies in Mathematics, Vikram University, Ujjain. M.P, INDIA, Email: Manoj.kumarjain@gmail.com
[2]Department of Mathematics, Govt Science College, Jabalpur, M. P., INDIA, Email: dalela@ymail.com
[3]School of Studies in Mathematics, Vikram University, Ujjain. M. P., INDIA, Email: skt_tiwari75@yahoo.co.in

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Cite: Manoj Kumar Jain, A. K. Dalela and Sandeep Kumar Tiwari, "Application of Fuzzy Mathematical Model in Assets-Liabilities," International Journal of Trade, Economics and Finance vol. 1, no. 3, pp. 247-253, 2010.

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