Dynamically consistent Choquet random walk and real investments
AbstractIn the real investments literature, the investigated cash flow is assumed to follow some known stochastic process (e.g. Brownian motion) and the criterion to decide between investments is the discounted utility of their cash flows. However, for most new investments the investor may be ambiguous about the representation of uncertainty. In order to take such ambiguity into account, we refer to a discounted Choquet expected utility in our model. In such a setting some problems are to dealt with: dynamical consistency, here it is obtained in a recursive model by a weakened version of the axiom. Mimicking the Brownian motion as the limit of a random walk for the investment payoff process, we describe the latter as a binomial tree with capacities instead of exact probabilities on its branches and show what are its properties at the limit. We show that most results in the real investments literature are tractable in this enlarged setting but leave more room to ambiguity as both the mean and the variance of the underlying stochastic process are modified in our ambiguous model
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HAL in its series Working Papers with number halshs-00533826.
Date of creation: 2010
Date of revision:
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00533826/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Choquet integrals; conditional Choquet integrals; random walk; Brownian motion; real options; optimal portfolio;
Other versions of this item:
- André Lapied & Robert Kast, 2010. "Dynamically consistent Choquet random walk and real investments," Working Papers, LAMETA, Universtiy of Montpellier 10-21, LAMETA, Universtiy of Montpellier, revised 2010.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Epstein, Larry G. & Schneider, Martin, 2003.
Journal of Economic Theory, Elsevier,
Elsevier, vol. 113(1), pages 1-31, November.
- Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
- Riedel, Frank, 2004.
"Dynamic coherent risk measures,"
Stochastic Processes and their Applications, Elsevier,
Elsevier, vol. 112(2), pages 185-200, August.
- Frank Riedel, 2003. "Dynamic Coherent Risk Measures," Working Papers, Stanford University, Department of Economics 03004, Stanford University, Department of Economics.
- Chateauneuf, A. & Kast, R. & Lapied, A., 1992.
"Choquet Pricing for Financial Markets with Frictions,"
G.R.E.Q.A.M., Universite Aix-Marseille III
92a11, Universite Aix-Marseille III.
- A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(3), pages 323-330.
- Robert Kast & André Lapied, 2010.
"Valuing future cash flows with non separable discount factors and non additive subjective measures: conditional Choquet capacities on time and on uncertainty,"
Theory and Decision, Springer,
Springer, vol. 69(1), pages 27-53, July.
- Robert Kast & André Lapied, 2008. "Valuing future cash flows with non separable discount factors and non additive subjective measures: Conditional Choquet Capacities on Time and on Uncertainty," Working Papers, LAMETA, Universtiy of Montpellier 08-09, LAMETA, Universtiy of Montpellier, revised Jun 2008.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 571-87, May.
- Robert Kast & André Lapied & Pascal Toquebeuf, 2008. "Updating Choquet Integrals , Consequentialism and Dynamic Consistency," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 04-2008, ICER - International Centre for Economic Research.
- Kast, R. & Lapied, A., 1997. "A Decision Theoretic Approach to Bid-Ask Spreads," G.R.E.Q.A.M., Universite Aix-Marseille III 97a17, Universite Aix-Marseille III.
- Itzhak Gilboa & David Schmeidler, 1991.
"Updating Ambiguous Beliefs,"
Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science
924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- De Waegenaere, Anja & Kast, Robert & Lapied, Andre, 2003. "Choquet pricing and equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 359-370, July.
- Kast, Robert & Lapied, André & Roubaud, David, 2014. "Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet–Brownian motions," Economic Modelling, Elsevier, Elsevier, vol. 38(C), pages 495-503.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.