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A Personal Financial Planning Model Based on

Fuzzy Multiple Goals Programming Method

Chieh-Yow ChiangLin

1

1

Department of Finance, National Kaohsiung University of Applied Sciences

Abstract

Traditional financial planning procedures began from taking into account the planner’s initial financial situation, his/her financial goals, and expectations for the future, etc. and then calculating the future cash flows for different time periods under variant scenarios. If the planning result cannot meet the planner’s expectation, then the planner has to adjust the tunable parameters continuously until obtaining an acceptable financial arrangement. Such a “trial-and-error” or so-called “what-if analysis” method does not promise to achieve an optimal planning result, and cannot afford to analyze how the financial plan will be modified when the parameters change. This paper proposes a generalized personal financial planning programming model with fuzzy multiple goals to solve the personal financial planning problem under a different way compared to the traditional methodology.

Keywords: personal financial planning, mathematical

programming, fuzzy multiple goals programming.

1. Introduction

Personal financial planning, in regards to the wealth holder as the decision center, tries to manage all money activities during a person’s lifetime, including maximizing one’s wealth, satisfying one’s life goals, and managing different sources of risk. Financial planning begins by measuring personal financial statements which could require that the planner provide financial data, his/her life goals, risk preferences, etc. By trial calculation under different scenarios, the planner can make a better decision for the wealth holder, but it might not be the best decision for non-trivial financial actions. Such a “what-if” analysis might present the following problems.

• Solving the financial planning problem by a “trial-and-error” method might obtain a satisfied suggestion, but may not achieve the best decision in the solution space. Even some

numerical analysis methods, for example, goal seeking, could be applied to find the best decision for single decision variable (Crabb, 2003). However, because financial planning includes many different dimensions and decision variables, a traditional tuning method is unable to cope with realistic situations. • The regulation of possible financial plans

might consider multiple goals, but traditional “what-if” analysis cannot handle it.

• Planners might possess various preference structures for different objectives.

• For the achieved level of each specific financial goal, it is not always a crisp binary state, rather a fuzzy continuous space.

As Fortin(1997) stated, the solution to financial planning might not be a closed-form solution. To resolve such difficulties, a mathematical programming method could be applied to meet the essence of planning, which is the main motivation for this research. By applying the mathematical programming method, the above problems could be solved.

This paper selects an integrated financial planning model quoted from[1] as an illustrative example to develop a general financial planning model. In this example, the decision variables include salary, living spending, cost of purchasing a home, raising children, and education expenses, etc. The financial planning mathematical model can cope with the aforementioned problems.

2. Numerical Example of Personal

Financial Planning

A numerical example is provided as follows.

Example 1:(quoted from [1])

Mr. Chiang, the planner, is 30 years old and his wife is 28 years old. They plan to have their first child after 2 years and have another one after 5 years. Yearly revenue for Mr. Chiang is about NT$600,000, and for Mrs. Chiang it is NT$400,000. Yearly living expenses

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alternative feasible solution spaces and achievement goal values for the two fuzzy goals.

Table 1: Planning results (Unit: NT$1,000)

Fig. 1: Membership functions of two decision

5. Conclusions and Further

Research

The mathematical programming model with fuzzy multiple goals is selected in this paper in order to propose a generalized personal financial planning model which includes the decision variables related to living expenses, revenue, buying a home, education planning, etc. Compared to the traditional “what-if” analysis used in the personal financial planning, the proposed method finds the optimal solution among different conflicting goals and tackles the fuzzy characteristics of the goals.

Fig. 2: Alternative feasible solution spaces and achievement goal values for two fuzzy goals

Based upon the model in this work, the following research directions can be suggested.

• Since the proposed framework is a non-linear mathematical programming model, a heuristic algorithm can be developed to find the global optimal solution.

• The preference structure among different goals can be considered in the proposed model and the preference weights for the decision maker can be detected by techniques, such as AHP (Analytic Hierarchy Process)(Saaty, 1980). • More facets of personal financial planning,

such as tax planning, insurance planning, estate planning, etc, can be considered in the model.

• Based on the model proposed in this paper, a decision support system can be developed to facilitate personal financial planning.

References

[1] Financial Planning Editorial Committee, Practice of Personal Financial Planning, Taiwan Academy of Banking and Finance (2003). (In Chinese) [2] R. Bellman and L. A. Zadeh, Decision-making in

a fuzzy environment, Management Science, Vol. 17B, pp. 141-164 (1970).

[3] N. Chieffe and G. K. Rakes, An integrated model for financial planning, Financial Service Review 8, pp. 261-268 (1999).

[4] R. R. Crabb, Cash flow: a quick and easy way to learn personal finance, Financial Service Review 8, pp. 269-282 (1999).

[5] R. Fortin, Retirement planning mathematics, Journal of Financial Education, 23 (1997), 73-80. [6] A. J. Keown, Personal finance: turning money

into wealth, 2nd ed. Prentice Hall (2001).

[7] H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, Col. 1, No. 1, pp. 45-56, (1978). Expense 340.00 345.00 350.00 355.00 360.00 365.00 House Price 9,900.00 9,801.00 9,696.40 9,564.10 9,431.81 9,299.51 Lamda -0.10 -0.05 0.00 0.05 0.10 0.15 Expense 370.00 375.00 380.00 385.00 390.00 395.00 House Price 9,167.22 9,034.92 8,902.62 8,770.33 8,637.62 8,364.23 Lamda 0.20 0.25 0.30 0.35 0.40 0.45 Expense 400.81 405.00 410.00 415.00 420.00 425.00 House Price 8,000.00 7,737.37 7,423.94 7,110.51 6,797.08 6,483.66 Lamda 0.51 0.55 0.60 0.65 0.70 0.62 Expense 430.00 435.00 440.00 445.00 450.00 455.00 House Price 6,170.23 5,856.80 5,543.37 5,229.94 4,916.51 4,603.08 Lamda 0.54 0.46 0.39 0.31 0.23 0.15 Expense 460.00 465.00 470.00 475.00 480.00 -- House Price 4,289.65 3,976.23 3,662.80 3,349.37 3,035.94 -- Lamda 0.07 -0.01 -0.08 -0.16 -0.24 --

數據

Fig. 1: Membership functions of two decision

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