The Optimization in Finance (Stocks)

2012

FINENG 511 HOMEWORK 1

FINENG 511 Homework -1 2012

QUESTION 1 Decision Variables : xi : The amount borrowed for 2 years at the beginning of quarter i yi : The amount borrowed for 2 quarters at the beginning of quarter i zi : The amount borrowed for 1 quarter at the beginning of quarter i Si : The surplus amount at the beginning of quarter i for every quarter i= 1,2,3,4,5,6,7,8,9.

Objective: Maximize S9

Constraints: i) ii) Cash inflow = Cash outflow at every quarter i Non negativity of decision variables.

Model:

x1 + y1 + z1 - S1 =100 y2 + z2 -0.01x1 - 0.018y1 - 1.025z1 + 1.005S1 - S2 = 500 y3 + z3 -0.01x1 - 0.018y2 - 1.018y1 - 1.025z2 + 1.005S2 - S3 = 100 y4 + z4 -0.01x1 - 0.018y3 - 1.018y2 - 1.025z3 + 1.005S3 - S4 = -600 y5 + z5 -0.01x1 - 0.018y4 - 1.018y3 - 1.025z4 + 1.005S4 - S5 = -500 y6 + z6 -0.01x1 - 0.018y5 - 1.018y4 - 1.025z5 + 1.005S5 - S6 = 200 y7 + z7 -0.01x1 - 0.018y6 -1.018y5 - 1.025z6 + 1.005S6 - S7 = 600 z8 -0.01x1 - 0.018y7 - 1.018y6 - 1.025z7 + 1.005S7 - S8 = -900

1

FINENG 511 Homework -1 2012

-0.01x1 - 1.018y7 - 1.025z8 + 1.005S8 - S9 = 0

QUESTION 2 a) By using solver in excel, Microsoft Excel 14.0 Answer Report Worksheet: [Hw1 q2.xlsx]Sheet1 Report Created: 1/18/2012 12:06:25 PM Result: Solver found a solution. All Constraints and optimality conditions are satisfied. Solver Engine Engine: Simplex LP Solution Time: 0.078 Seconds. Iterations: 2 Subproblems: 0 Solver Options Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Max) Cell $E$7 total Name Original Value 350 Final Value 350

Variable Cells Cell $C$4 $D$4 Name x1 x2 Original Value 50 50 Final Value Integer 50 Contin 50 Contin

Constraints Cell $E$10 $E$11 $E$12 Name alloc constr ratings constr maturity constr Cell Value Formula 100 $E$10 B=[100;150;360;0;0] B= 100 150 360 0 0

4

FINENG 511 Homework...