1. University of Economics, Faculty of Informatics Dolnozemská cesta 1, 852 35 Bratislava Slovak Republic Financial Mathematics in Derivative Securities and Risk Reduction Investment Schedul Ass. Prof. Ľudovít Pinda, CSc. Department of Mathematics, Tel.:++421 2 67295 813, ++421 2 67295 711 Fax:++421 2 62412195 e-mail: pinda@dec.euba.sk

2. Sylabus of the lecture The investment schedul. Indifference curves. The optimal investment decision. The money market line. The including the indifference map into the concept.

3. The investment schedul Tab. 1

4. Productivity curve d b a Project A Project B Project C Project D C 1 1 265 950 350 200 0 Fig. 1 W 0 =1 000 C 0

6. Optimal investment decision

7. C 1 d C 1 * 0 I2I1I2I1 C 0 * W 0 C 0 C* I0I0 Fig. 3 The money market line k – opportunity cost of capital,

8. Fig. 4

10. Fig. 5 0 C 0 ** C 0 * W 0 C 0 C** C* I2I2 I1I1 L I 0 C 1  C 1  The icluding the indifference map into the concept 1.The point of tangency with the indifference curve lie to the left of point C *

11. C * - the point of tangency between the highst attainable iso-PV line and the productivity curve, W 0 C * - the accepted projects as the segment of productive curve, C * ( I 1 ) – lies below I 2. For finding a higher rate of satisfaction we lend the amount L at the opportunity cost of capital k. This is indicated by a movement along the iso-PV line to C ** at which point the iso-PV line is tangent to indifference curve I 2. The return for the loan is L( 1+k ).

12. 2. The point of tangency with the indifference curve lie to the right of point C * Fig. 6 W 0 C * - the accepted projects as the segment of productive curve, I 0 – the initial investment for achieving C * and borrow the amound B in order to increase his current consumption, I1I1 I2I2 C* C** C1*C1* C 1 ** I 0 B C 0  W 0 C 0 