Maximum Entropy Principle with General Deviation Measures

References

• Artzner P., Delbaen F., Eber J.-M., Heath D. Coherent measures of risk. Math. Finance (1999) 9:203–227Crossref, Google Scholar
• Bialas J., Nakamura Y. The theorem of Weierstrass. J. Formalized Math. (1996) 5(3):353–359Google Scholar
• Benoist J., Daniilidis A. Coincidence theorems for convex functions. J. Convex Anal. (2002) 9(1):259–268Google Scholar
• Brody D. C., Buckley Ian R. C., Constantinou I. C. Option price calibration from Rényi entropy. Phys. Lett. A (2007) 366:298–307Crossref, Google Scholar
• Buchen P., Kelly M. The maximum entropy distribution of an asset inferred from option prices. J. Financial Quant. Anal. (1996) 31(1):143–159Crossref, Google Scholar
• Costa J., Hero A., Vignat C., Rangarajan A., Figueiredo M., Zerubia J. On solutions to multivariate maximum-entropy problems. Lecture Notes in Computer Science (2003) 2683(Springer-Verlag, Berlin) 211–228Google Scholar
• Cover T. M., Thomas J. A.Elements of Information Theory (1991) 1st ed.(Wiley, New York) Crossref, Google Scholar
• Cozzolino J. M., Zahner M. J. The maximum-entropy distribution of the future market price of a stock. Oper. Res. (1973) 21(6):1200–1211Link, Google Scholar
• Dana R.-A. A representation result for concave Schur-concave functions. Math. Finance (2005) 15(4):613–634Crossref, Google Scholar
• Follmer H., Schied A.Stochastic Finance: An Introduction in Discrete Time (2004) 2nd ed.(de Gruyter, Berlin) Crossref, Google Scholar
• Friedman C., Huang J., Sandow S. A utility-based approach to some information measures. Entropy (2007) 9:1–6Crossref, Google Scholar
• Jaynes E. T. Prior probabilities. IEEE Trans. Systems Sci. Cybernetics (1968) 4:227–251Crossref, Google Scholar
• Jaynes E. T. Information theory and statistical mechanics. Physical Rev. (1957) 106(4):620–630Crossref, Google Scholar
• Johnson O., Vignat C. Some results concerning maximum Rényi entropy distributions. Annales de l'Institute Henri Poincare (B) Probab. Statist. (2007) 43(3):339–351Crossref, Google Scholar
• Jouini E., Schachermayer W., Touzi N. Law invariant risk measures have the Fatou property. Adv. Math. Econom. (2006) 9:49–71Crossref, Google Scholar
• Kusuoka S. On law invariant coherent risk measures. Adv. Math. Econom. (2001) 3:83–95Crossref, Google Scholar
• Lutwak E., Yang D., Zhang G. Cramer-Rao and moment-entropy inequalities for Rényi entropy and generalized Fisher information. IEEE Trans. Inform. Theory (2005) 51:473–478Crossref, Google Scholar
• Markowitz H. M. Portfolio selection. J. Finance (1952) 7(1):77–91Google Scholar
• Rényi A. On measures of information and entropy. Proc. 4th Berkeley Sympos. Math. Statist. Probab. (1961) (University of California Press, Berkeley) 547–561Google Scholar
• Rockafellar R. T., Uryasev S. Optimization of conditional value-at-risk. J. Risk (2000) 2:21–41Crossref, Google Scholar
• Rockafellar R. T., Uryasev S., Zabarankin M. Deviation measures in risk analysis and optimization. (2002) . Research Report 2002-7, Department of Industrial and Systems Engineering, University of Florida, GainesvilleGoogle Scholar
• Rockafellar R. T., Uryasev S., Zabarankin M. Generalized deviations in risk analysis. Finance Stochastics (2006) 10(1):51–74Crossref, Google Scholar
• Rockafellar R. T., Uryasev S., Zabarankin M. Optimality conditions in portfolio analysis with general deviation measures. Math. Programming (2006a) 108(2–3):515–540Crossref, Google Scholar
• Rockafellar R. T., Uryasev S., Zabarankin M. Master funds in portfolio analysis with general deviation measures. J. Banking Finance (2006b) 30(2):743–777Crossref, Google Scholar
• Rockafellar R. T., Uryasev S., Zabarankin M. Equilibrium with investors using a diversity of deviation measures. J. Banking Finance (2007) 31(11):3251–3268Crossref, Google Scholar
• Rockafellar R. T., Uryasev S., Zabarankin M. Risk tuning with generalized linear regression. Math. Oper. Res. (2008) 33(3):712–729Link, Google Scholar
• Rudloff B. Hedging in incomplete markets and testing compound hypotheses via convex duality. (2006) . Dissertation, Martin-Luther University Halle-Wittenberg, Halle, GermanyGoogle Scholar
• Shannon C. E. A mathematical theory of communication. Bell System Tech. J. (1948) 27:379–423623656Crossref, Google Scholar
• Stutzer M. A simple nonparametric approach to derivative security valuation. J. Finance (1996) 51(5):1633–1652Crossref, Google Scholar
• Thomas M. U. A generalized maximum entropy principle. Oper. Res. (1979) 27(6):1188–1196Link, Google Scholar
• Willard S.General Topology (2004) (Courier Dover Publications, Mineola, NY) Google Scholar