Browse > Article
http://dx.doi.org/10.14317/jami.2011.29.3_4.987

OPTIMAL PARTIAL HEDGING USING COHERENT MEASURE OF RISK  

Kim, Ju-Hong (Department of Mathematics, Sungshin Women's University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.3_4, 2011 , pp. 987-1000 More about this Journal
Abstract
We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where $\tilde{\psi}$ is a randomized test in the static problem. Coherent risk measure is used as risk measure in the $L^{\infty}$ random variable spaces. The paper is written in expository style to some degree. We use an average risk of measure(AVaR), which is a special coherent risk measure, to see how to hedge the modified claim in a complete market model.
Keywords
coherent risk measure; optimal hedging; incomplete markets; Neyman-Pearson lemma;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Y. Nakano, Effcient hedging with coherent risk measures, Journal of Mathematical Analysis and Applications 293(2004), 345-354.   DOI   ScienceOn
2 N. El Karoui and M. C. Quenez, Dynamic programming and pricing of contingent claims in an incomplete market, SIAM J. Control and Optimization 33 (1995), 29-66.   DOI   ScienceOn
3 D. O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in an incomplete security market, Probability Theory and Related Fields 105 (1996), 459-479.   DOI   ScienceOn
4 H. Follmer and P. Leukert, Quantile hedging, Finance and Stochastics 10 (1999), 163-181.
5 P. Artzner, F. Delbaen, J.-M, Eber and D. Heath, Coherent measures of risk, Mathematical Finance 9(1999), 203-223.   DOI
6 H. Follmer and P. Leukert, Effcient hedging: Cost versus shortfall risk, Finance and Stochastics 4 (2000), 117-146.   DOI   ScienceOn
7 H. Follmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time, Springer- Verlag, New York, 2002.
8 I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1991.
9 F. Delbaen and W. Schachermayer, A General version of the fundamental theorem of asset pricing, Mathematische Annalen 300 (1994), 463-520.   DOI   ScienceOn
10 F. Delbaen, Coherent risk measures on general probability spaces, Advances in finance and stochastics: Essays in honor of Dieter Sondermann (2002), Springer, 1-37.
11 T. Arai, Good deal bounds induced by shortfall risk, preprint (2009).