본문 바로가기
KERD
논문KCI 등재

SHORTFALL RISK MINIMIZATION: THE DUAL APPROACH

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maxi-mization problem is used and we get the same results as in the paper [21].

Abstract

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maxi-mization problem is used and we get the same results as in the paper [21].

참고문헌 (23)

  1. T. Arai, "Good deal bounds induced by shortfall risk", ~ (2009)
  2. M. Avriel, "Nonlinear Programming: Analysis and Methods" (2003), Dover Publications, Inc
  3. P. Artzner, "Coherent measures of risk", Mathematical Finance, 9, pp.203~223 (1999)
  4. F. Bellini, "Utility maximization in incomplete markets for unbounded processes", Mathematical Finance, 21, pp.1~21 (2002)
  5. F. Bellini, "On the existence of minimax martingale measures", Finance Stoch, 9, pp.493~517 (2005)
  6. J. Cvitanic, "Minimizing expected loss of hedging in incomplete and constrained markets", SIAM J. Control Optim, 38, pp.1050~1066 (2000)
  7. J. Cvitanic, "On dynamic measures of risk", Finance Stoch, 3, pp.451~482 (1999)
  8. F. Delbaen, "Coherent risk measures on general probability spaces. Advances in nance and stochastics: Essays in honor of Dieter Sondermann", pp.1~37 (2002), Springer
  9. F. Delbaen, "A General version of the fundamental theorem of asset pricing", Mathematische Annalen, 300, pp.463~520 (1994)
  10. F. Delbaen, "The fundamental theorem of asset pricing for unbounded stochastic processes", Mathematische Annalen, 312, pp.463~520 (1994)
  11. H. FÄollmer, "Quantile hedging", Finance and Stochastics, 10, pp.215~250 (1999)
  12. H. FÄollmer, "Effcient hedging: Cost versus shortfall risk", Finance and Stochastics, 4, pp.117~146 (2000)
  13. H. FÄollmer, "Stochastic Finance: An Introduction in Discrete Time" (2002), Springer-Verlag
  14. I. Karatzas, "Brownian Motion and Stochastic Calculus" (1991), Springer-Verlag
  15. N. El Karoui, "Dynamic programming and pricing of contingent claims in an incomplete market", SIAM J. Control and Optimization, 33, pp.29~66 (1995)
  16. I. Karatzas, "Martingale and duality methods for utility maximization in an incomplete market", SIAM J. Control and Optimization, 29, pp.702~730 (1991)
  17. 김주홍, "OPTIMAL PARTIAL HEDGING USING COHERENT MEASURE OF RISK", Journal of Applied Mathematics and Informatics, 29(3), pp.987~1000 (2011), 한국전산응용수학회
  18. D.O. Kramkov, "Optional decomposition of supermartingales and hedging contingent claims in an incomplete security market", Probability Theory and Related Fields, 105, pp.459~479 (1996)
  19. Y. Nakano, "Effcient hedging with coherent risk measures", J. Math. Anal. Appl, 293, pp.345~354 (2004)
  20. H. Pham, "Dynamic LP -hedging in descrete-time under cone constraints", SIAM J. Con- trol and Optimization, 38, pp.665~682 (2000)
  21. H. Pham, "Minimizing shortfall risk and applications to finance and insurance problems", Annals of Applied Probability, 12, pp.143~172 (2002)
  22. R.T. Rockfellar, "Conjugate Duality and Optimization", Conference Board of Math. Sciences Series (1974), SIAM Publications
  23. G. Spivak, "Maximizing the probability of a perfect hedge", Annals of Applied Probability, 9, pp.1303~1328 (2002)

이 간행물의 다른 논문 (9건)