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Annals of Finance

, Volume 14, Issue 2, pp 211–221 | Cite as

Financial equilibrium with non-linear valuations

  • Dilip B. Madan
Research Article

Abstract

Classical Arrow Debreu equilibria employ budget feasibility to require individuals to ensure excess supplies to be nonnegative in value using the single equilibrium price system for valuation purposes. Yet by the selection of state contingent prices, they seek excess supplies that are nonnegative in each component, and not just the value. A financial equilibrium, on the other hand, defines acceptable economic risks as excess supplies that are nonnegative in value for a number of prespecified valuation price systems. The collection of prespecified valuation price systems may be referred to as features for which clearing is sought. The number of features will generally be less than the number of states. It is then shown that by also defining budget feasibility nonlinearly one may construct a financial equilibrium with fewer securities than there are features to be cleared.

Keywords

Acceptable risks Nonlinear conditional expectation Conic finance Two price economy 

JEL Classification

G10 G12 G13 D50 D51 

References

  1. Aliprantis, C.D., Tourky, R., Yannelis, N.C.: A theory of value with non-linear prices. J Econ Theory 100, 22–72 (2001)CrossRefGoogle Scholar
  2. Arrow, K.J., Debreu, G.: Existence of equilibrium for a competitive economy. Econometrica 22, 256–290 (1954)Google Scholar
  3. Arrow, K.J., Hahn, F.H.: General Competitive Analysis. Holden-Day, San Francisco (1971)Google Scholar
  4. Artzner, P., Delbaen, F., Eber, M., Heath, D.: Coherent measures of risk. Math Finance 9, 203–228 (1999)CrossRefGoogle Scholar
  5. Baily, M.N., Elliott, D.J.: The Role of Finance in the Economy: Implications of Structural Reform of the Financial Sector. Brookings Institution, Washington, DC. http://www.brookings.edu/~/media/research/files/papers/2013/07/11-finance-role-in-economy-baily-elliott/11-finance-role-in-economy-baily-elliott.pdf (2013)
  6. Breeden, D., Litzenberger, R.H.: Prices of state-contingent claims implicit in option prices. J Bus 51, 621–751 (1978)CrossRefGoogle Scholar
  7. Cohen, S., Elliott, R.J.: A general theory of backward finite state difference equations. Stoch Process Appl 120, 442–466 (2010)CrossRefGoogle Scholar
  8. Debreu, G.: Theory of Value. Yale University Press, New Haven (1959)Google Scholar
  9. Drèze, J.H.: Uncertainty and the firm in general equilibrium theory. Econ J 95, 1–20 (1985)CrossRefGoogle Scholar
  10. Duffie, D., Huang, C.F.: Implementing Arrow–Debreu equilibria by continuous trading of few long lived securities. Econometrica 53, 1337–1356 (1985)CrossRefGoogle Scholar
  11. Eberlein, E., Madan, D.B., Pistorius, M., Yor, M.: Bid and ask prices as non-linear continuous time G-expectations based on distortions. Math Financ Econ 8, 265–289 (2014)CrossRefGoogle Scholar
  12. Eberlein, E., Madan, D.B., Pistorius, M., Schoutens, W., Yor, M.: Two price economies in continuous time. Ann Finance 10, 71–100 (2014)CrossRefGoogle Scholar
  13. Grandmont, J.M.: Temporary general equilibrium. Econometrica 45, 535–572 (1977)CrossRefGoogle Scholar
  14. Keen, S.: Finance and economic breakdown: modeling Minsky’s financial instability hypothesis. J Post Keynes Econ 17, 607–635 (1995)CrossRefGoogle Scholar
  15. Keynes, J.M.: The General Theory of Employment, Interest and Money. Macmillan, London (1936)Google Scholar
  16. Keynes, J.M.: The general theory of employment. Q J Econ 51, 209–223 (1937)CrossRefGoogle Scholar
  17. Kusuoka, S.: On law invariant coherent risk measures. Adv Math Econ 3, 83–95 (2001)CrossRefGoogle Scholar
  18. Madan, D.B.: A two price theory of financial equilibrium with risk management implications. Ann Finance 8, 489–505 (2012)CrossRefGoogle Scholar
  19. Madan, D.B.: Asset pricing theory for two price economies. Ann Finance 11, 1–35 (2015)CrossRefGoogle Scholar
  20. Madan, D.B.: Benchmarking in two price financial markets. Ann Finance 12, 201–219 (2016)CrossRefGoogle Scholar
  21. Madan, D.B., Schoutens, W.: Applied Conic Finance. Cambridge University Press, Cambridge (2016)CrossRefGoogle Scholar
  22. Madan, D.B., Schoutens, W.: Conic option pricing. J Deriv 25, 10–36 (2017)CrossRefGoogle Scholar
  23. Magill, M., Quinzii, M.: Theory of Incomplete Markets. MIT Press, Cambridge (1996)Google Scholar
  24. Milne, F.: Arbitrage and diversification in a general equilibrium asset economy. Econometrica 56, 815–840 (1985)CrossRefGoogle Scholar
  25. Minsky, H.M.: Inflation, Recession and Economic Policy. Wheatsheaf, Sussex (1982)Google Scholar
  26. Minsky, H.M.: Stablizing an Unstable Economy. Yale University Press, New Haven (1986)Google Scholar
  27. Peng, S.: Dynamically Consistent Nonlinear Evaluations and Expectations. Preprint No. 2004-1, Institute of Mathematics, Shandong University. arXiv:math/0501415v1 [math.PR] (2004)
  28. Peng, S.: G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type. arXiv:math/0601035v2 [math.PR] (2006)
  29. Peng, S.: Nonlinear Expectations and Stochastic Calculus under Uncertainty. arXiv:1002.4546 [math.PR] (2010)

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege ParkUSA

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