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금융수학 v.s. 금융공학

금융수학 v.s. 금융공학. 카이스트 수리과학과 강완모. Risk and Return. 금융공학적 접근 가능한 적은 Risk 를 가지고 가능한 많은 Return 을 얻고자 함 금융수학적 접근 Riskless (Risk-free) Return. Portfolio Optimization. maximize Return under a control of Risk minimize Risk under a guarantee of some Return. What measures of Risk?.

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금융수학 v.s. 금융공학

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  1. 금융수학 v.s. 금융공학 카이스트 수리과학과 강완모 KAIST-IE

  2. Risk and Return • 금융공학적 접근 • 가능한 적은 Risk를 가지고 가능한 많은 Return을 얻고자 함 • 금융수학적 접근 • Riskless (Risk-free) Return KAIST-IE

  3. Portfolio Optimization • maximize Return under a control of Risk • minimize Risk under a guarantee of some Return KAIST-IE

  4. What measures of Risk? • Standard Deviation, Variance • VaR (Value at Risk), Shortfall • Coherent Risk Measure KAIST-IE

  5. Portfolio Optimization • Max s.t. KAIST-IE

  6. 이항모형 • Binomial Asset-Pricing Model 확률변수 분포 Q: 0과 1사이의 시간 간격은? Q: 와 의 관계는? KAIST-IE

  7. 이항모형 • Binomial Asset-Pricing Model Risky Asset Risk-free Asset KAIST-IE

  8. 이항모형 • Binomial Asset-Pricing Model Risky Asset Risk-free Asset KAIST-IE

  9. How to make Money 싸게 사서 비싸게 판다 At time 0: 1.Short of bank account 2.Long one share of stock At time 1: 3.Take at least of without any RISK ARBITRAGE!!! KAIST-IE

  10. It’s simple 싸게 사서 비싸게 판다 At time 0: 1.Short one share of stock 2.Long of bank account At time 1: 3.Take at least of without any RISK KAIST-IE

  11. No Way!!! At time 0: At time 1: NO RISKLESS RETURN if KAIST-IE

  12. 새로운 금융상품 KAIST-IE

  13. 확대된 금융시장 + KAIST-IE

  14. 만약에… = = = KAIST-IE

  15. 만약에… = + = + = + KAIST-IE

  16. 선형대수학? Return on T Return on H KAIST-IE

  17. 뺄셈… = + = + - KAIST-IE

  18. 대입… = + KAIST-IE

  19. 대입… = + KAIST-IE

  20. 정리하면… KAIST-IE

  21. Risk-Neutral Probability Q KAIST-IE

  22. Risk-Neutral Probability Q V.S. KAIST-IE

  23. Complete Market Return on T Return on H KAIST-IE

  24. Complete Market Return on T Return on H KAIST-IE

  25. Incomplete Market ??? Return on T Return on M Return on H KAIST-IE

  26. No Arbitrage in Multi-states • Farkas’ lemma If is a matrix and , then exactly one of the following alternatives holds • There is a non-negative solution of . • The inequalities and have a solution . KAIST-IE

  27. Too Simple? KAIST-IE

  28. Harrison and Pliska • Martingales and Stochastic integrals in the theory of continuous trading • Michael Harrison: Stanford OR Ph.D. • Stanley Pliska: Stanford OR Ph.D. • Approximating queuing system using Brownian motion. KAIST-IE

  29. Want to be a Financial Engineer? KAIST-IE

  30. Want to be a Financial Engineer? KAIST-IE

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