1. University of Economics, Faculty of Informatics Dolnozemská cesta 1, 852 35 Bratislava Slovak Republic Financial Mathematics in Derivative Securities and Risk Reduction Insurance and Risk Reduction, Financial Layering 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 lectures  Preloss financing: - Retention funding.  Composite financing strategies: - Full insurance and partial insurence. - Insurance and risk reduction : - Risk reduction with coinsurance. - Risk reduction with deductibles.  Financial layering.

3. Identify Risk, Management Events: Measure Capital Costs Estimate Effects on Corporate Earnings and Cost of Capital Immediate Investment Decision Contingent Investment Decision Loss Reduction No Loss Reduction Postloss Reinvestment Postloss Abandonment Financing Postloss Financing Preloss Financing Dept Equity Internal funds Dept Equity Internal funds Insurance Contingent Loans Funding Tab. 1 Decision Framework for financial Risk Management

4. Retention funds when alternative sources of finance have no transaction costs

8. The value of the firm:  The commercial non-risk management activities.  The value of retention fund.  The value of the firms loss exposure. Retention funds when the alternative sources of finance have transaction costs

9. The value of the firm: The value from commercial non-risk management activities. The value or cost from establishing a fund and investing its assets minus the cost of raising capital to finance the fund. The ( negative ) value contributed by the loss exposure. The ( negative ) contribution to value arising from the prospect of incurring transaction costs for unfunded loses.

10. Composite financing strategies Full insurance and partial insurance Fig. 1 Loss distribution and Proportionale Coinsurance

11. Risk Reduction with Coinsurance

15. Example 1 Solution Tab. 1

16. Tab. 2

17. Tab. 3

18. Fig. 2 Fig. 3

19.  =0,75  =0,5  =0,25  =0  =1 )(E   17,3 17,4 17,5 17,6 17,7 17,8 8,599,51010,511 E(E) cov(X,L)=20 cov(X,L)=0 Fig. 4

20. Settlement under policy with 20 000 deductibles Per loss deductibleCumulative deductible LossPayment Cumulative loss Payment 16 0000173 000173 000-20 000=153 000 33 00033 000-20 000=13 000 124 000124 000-20 000=104 000 Total settlement 117 000153 000 Risk reduction with deductibles Tab. 4

21. Fig. 5 Distribution of retained loss Distribution of policy payment

23. Example 2 The loss distribution by Tab. 5 l0100100010 00020 000 p(l)0.60.60.20.20.10.10.040.06 Tab. 5

25. Tab. 6 12200 12400 12600 12800 13000 13200 13400 100020003000400050006000 E(E) Fig. 6

26. Financial Layering Tab. 7

27. C L 0 C=L L C 0 C Insurance New Issue Fig. 7Fig. 8 Internal Liquid Resources C L 0 C=L Fig. 9

28. Two-layer financing methods Fig. 10

29. Three-layer financing method Tab. 8 Fig. 11