NEYMAN-PEARSON THEORY AND ITS APPLICATION TO SHORTFALL RISK IN FINANCE
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Shortfall risk is considered by taking some exposed risks because the superhedging price is too expensive to be used in practice. Minimizing shortfall risk can be reduced to the problem of finding a randomized test ψ in the static problem. The optimization problem can be solved via the classical Neyman-Pearson theory, and can be also explained in terms of hypothesis testing. We introduce the classical Neyman-Pearson lemma expressed in terms of mathematics and see how it is applied to shortfall risk in finance.
Abstract
Shortfall risk is considered by taking some exposed risks because the superhedging price is too expensive to be used in practice. Minimizing shortfall risk can be reduced to the problem of finding a randomized test ψ in the static problem. The optimization problem can be solved via the classical Neyman-Pearson theory, and can be also explained in terms of hypothesis testing. We introduce the classical Neyman-Pearson lemma expressed in terms of mathematics and see how it is applied to shortfall risk in finance.
참고문헌 (21)
- T. Arai, "Good deal bounds induced by shortfall risk", ~ (2009)
- P. Artzner, "Thinking coherently", RISK, 10, pp.68~71 (1997)
- P. Artzner, "Coherent measures of risk", Mathematical Finance, 9, pp.203~223 (1999)
- P. Cheridito, "Risk measures on Orlicz hearts", Mathematical Finance, 19, pp.189~214 (2009)
- J. Cvitanic, "Minimizing expected loss of hedging in incomplete and constrained markets", SIAM J. Control Optim, 38, pp.1050~1066 (2000)
- J. Cvitanic, "On dynamic measures of risk", Finance Stoch, 3, pp.451~482 (1999)
- J. Cvitanic, "Generalized Neyman-Pearson lemma via convex duality", Bernoulii, 7, pp.79~97 (2001)
- F. Delbaen, "Coherent risk measures on general probability spaces, In Advances in ¯nance and stochastics: Essays in honor of Dieter Sondermann", pp.1~37 (2002), Springer
- F. Delbaen, "A general version of the fundamental theorem of asset pricing", Mathematische Annalen, 300, pp.463~520 (1994)
- H. Follmer, "Quantile hedging", Finance and Stochastics, 10, pp.163~181 (1999)
- H. Follmer, "Efficient hedging: Cost versus shortfall risk", Finance and Stochastics, 4, pp.117~146 (2000)
- H. Follmer, "Stochastic Finance, An Introduction in Discrete Time, 2nd Edition, de Gruyter Studies in Mathematics 27" (2002), Springer-Verlag
- I. Karatzas, "Brownian Motion and Stochastic Calculus" (1991), Springer-Verlag
- 김주홍, "OPTIMAL PARTIAL HEDGING USING COHERENT MEASURE OF RISK", Journal of Applied Mathematics and Informatics, 29(3), pp.987~1000 (2011), 한국전산응용수학회
- 김주홍, "COHERENT AND CONVEX HEDGING ON ORLICZ HEARTS IN INCOMPLETE MARKETS", Journal of Applied Mathematics and Informatics, 30(3), pp.413~428 (2012), 한국전산응용수학회[DOI]
- E.L. Lehman, "Testing Statistical Hypotheses" (2005), Springer-Verlag
- Y. Nakano, "Minimizing coherent risk measures of shortfall in discrete-time models under cone constraints", Applied Mathematical Finance, 10, pp.163~181 (2003)
- Y. Nakano, "Efficient hedging with coherent risk measures", J. Math. Anal. Appl, 293, pp.345~354 (2004)
- B. Rudloff, "Convex hedging in incomplete markets", Applied Mathematical Finance, 14, pp.437~452 (2007)
- B. Rudloff, "Coherent hedging in incomplete markets", Quantitative Finance, 9, pp.197~206 (2009)
- A. Schied, "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals", The Annals of Applied Probability, 14, pp.1398~1423 (2004)