Balbás, Alejandro and Balbás, Raquel and Garrido, José (2008) Extending Pricing Rules with General Risk Functions. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
- Published Version
The paper addresses pricing issues in imperfect and/or incomplete markets if the risk level of the hedging strategy is measured by a general risk function. Convex
Optimization Theory is used in order to extend pricing rules for a wide family of risk functions, including Deviation Measures, Expectation Bounded Risk Measures and Coherent Measures of Risk. For imperfect markets the extended pricing rules reduce the bid-ask spread. The paper ends by particularizing the findings so as to study with more detail some concrete examples, including the Conditional Value at Risk and some properties of the Standard Deviation.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Authors:||Balbás, Alejandro and Balbás, Raquel and Garrido, José|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 4/08|
|Corporate Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||Incomplete and imperfect market, Risk measure and deviation measure, Pricing rule, Convex optimization|
|Deposited By:||DIANE MICHAUD|
|Deposited On:||02 Jun 2010 16:05|
|Last Modified:||08 Dec 2010 23:20|
Alexander, S., T.F. Coleman and Y. Li, 2006. “Minimizing CV aR and V aR for a portfolio of derivatives”. Journal of Banking & Finance, 30, 538-605.
Artzner, P., F. Delbaen, J.M. Eber and D. Heath, 1999. “Coherent measures of risk”. Mathematical Finance, 9, 203-228.
Balbás, A., B. Balbás and A. Heras, 2008a. “Optimal reinsurance with general risk functions”. Concordia University, Department of Mathematics and Statistics,
Technical Report 3/08. Montréal, Québec, Canada (also available at www.gloriamundi.org).
Balbás, A., R. Balbás and S. Mayoral, 2008b. “Portfolio choice problems and optimal hedging with general risk functions: A simplex-like algorithm”. European Journal of Operational Research (forthcoming).
Calafiore, G.C., 2007. “Ambiguous risk measures and optimal robust portfolios”. SIAM Journal on Optimization, 18, 3. 853-877.
Cherny, A.S., 2006. “Weighted V @R and its properties”. Finance & Stochastics, 10, 367-393.
Cochrane, J.H. and J. Saa-Requejo, 2000. “Beyond arbitrage: Good-deal asset price bounds in incomplete markets”. Journal of Political Economy, 108, 79-119.
De Wagenaere, A. and P.P. Wakker, 2001. “Nonmonotonic Choquet Integrals”. Journal of Mathematical Economics, 36, 1, 45-60.
Frittelli, M. and G. Scandolo, 2005. “Risk measures and capital requirements for processes”. Mathematical Finance, 16, 4, 589-612.
Goovaerts, M., R. Kaas, J. Dhaene and Q. Tang, 2004. “A new classes of consistent risk measures”. Insurance:Mathematics and Economics, 34, 505-516.
Horvàth, J., 1966. “Topological vector spaces and distributions, vol I” Addison Wesley, Reading, MA.
Jaschke, S. and U. Küchler, 2001. “Coherent risk measures and good deal bounds”. Finance & Stochastics, 5, 181-200.
Jouini, E. and H. Kallal, 1995. “Martingales and Arbitrage in Securities Markets with Transaction Costs”. Journal of Economic Theory, 66, 178-197.
Luenberger, D.G.,1969. “Optimization by vector spaces methods”. John Wiley & Sons, New York.
Luenberger, D.G., 2001, “Projection pricing”. Journal of Optimization Theory and Applications, 109, 1-25.
Mansini, R., W. Ogryczak and M.G. Speranza, 2007.
“Conditional value at risk and related linear programming models for portfolio optimization”. Annals of Operations Research, 152, 227-256.
Nakano, Y., 2004. “Efficient hedging with coherent risk measure”. Journal of Mathematical Analysis and Applications, 293, 345-354.
Ogryczak,W. and A. Ruszczynski, 2002. “Dual stochastic dominance and related mean risk models”. SIAM Journal on Optimization, 13, 60-78.
Rockafellar, R.T., S. Uryasev and M. Zabarankin, 2006.
“Generalized deviations in risk analysis”. Finance & Stochastics, 10, 51-74.
Schied, A., 2007. “Optimal investments for risk- and ambiguity-averse preferences: A duality approach”. Finance & Stochastics, 11, 107-129.
Schweizer, M., 1995. “Variance-optimal hedging in discrete time”. Mathematics of Operations Research, 20. 1, 1-32.
Staum, J. 2004. “Fundamental theorems of asset pricing for good deal bounds”. Mathematical Finance, 14, 141-161.
Wang, S.S., 2000. “A class of distortion operators for pricing financial and insurance risks”. Journal of Risk and Insurance, 67, 15-36.
Zalinescu, C., 2002. “Convex analysis in general vector spaces”. World Scientific Publishing Co.
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