Access the full text.
Sign up today, get DeepDyve free for 14 days.
Jan Dhaene, S. Vanduffel, M. Goovaerts, R. Kaas, D. Vyncke (2005)
Comonotonic Approximations for Optimal Portfolio Selection ProblemsRisk Management
H. Föllmer, A. Schied (2002)
Stochastic Finance: An Introduction in Discrete Time
(1999)
Private communication
Jan Dhaene, S. Vanduffel, M. Goovaerts, R. Kaas, Q. Tang, D. Vyncke (2006)
Risk Measures and Comonotonicity: A ReviewStochastic Models, 22
Carlier (2006)
Law Invariant Concave Utility Functions and Optimization Problems with Monotonicity and Comonotonicity ConstraintsStat. Decis, 24
(1993)
A continuous time version of Kulldorff’s resu lt
Hanqing Jin, Xun Zhou (2007)
BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIMEMathematical Finance, 18
R. Thaler (1980)
Toward a positive theory of consumer choiceJournal of Economic Behavior and Organization, 1
H. Föllmer, P. Protter (2000)
On Itô s formula for multidimensional Brownian motionProbability Theory and Related Fields, 116
W. Marsden (2012)
I and J
M. Hamada, M. Sherris, J. Hoek (2001)
Martingale Methods in Dynamic Portfolio Allocation with Distortion Operators-Proceedings AFIR 2001-Toronto, Canada
G. Carlier, R. Dana (2006)
Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraintsStatistics & Risk Modeling, 24
S. Browne (2000)
Risk-Constrained Dynamic Active Portfolio ManagementManagement Science, 46
Lopes Lopes (1987)
Between Hope and Fear: The Psychology of RiskAdv. Exp. Social Psychol, 20
Lola Lopes, G. Oden (1999)
The Role of Aspiration Level in Risky Choice: A Comparison of Cumulative Prospect Theory and SP/A Theory.Journal of mathematical psychology, 43 2
S. Kataoka (1963)
A Stochastic Programming ModelEconometrica, 31
P. Samuelson (1969)
LIFETIME PORTFOLIO SELECTION BY DYNAMIC STOCHASTIC PROGRAMMING
M. Machina (1982)
"Expected Utility" Analysis without the Independence AxiomEconometrica, 50
Sanjiv Das, H. Markowitz, J. Scheid, M. Statman (2010)
Portfolio Optimization with Mental AccountsJournal of Financial and Quantitative Analysis, 45
J. Harrison, David Kreps (1979)
Martingales and arbitrage in multiperiod securities marketsJournal of Economic Theory, 20
D. Kramkov, W. Schachermayer (1999)
The asymptotic elasticity of utility functions and optimal investment in incomplete marketsAnnals of Applied Probability, 9
D. Kahneman, A. Tversky (1979)
Decision, probability, and utility: Prospect theory: An analysis of decision under risk
Gennady Spivak, Jakša Cvitanić (1999)
Maximizing the probability of a perfect hedgeAnnals of Applied Probability, 9
Jakša Cvitanić, I. Karatzas (1992)
Convex Duality in Constrained Portfolio OptimizationAnnals of Applied Probability, 2
M. Hamada, M. Sherris, J. Hoek (2006)
Dynamic Portfolio Allocation, the Dual Theory of Choice and Probability Distortion FunctionsASTIN Bulletin, 36
J. Quiggin (1982)
A theory of anticipated utilityJournal of Economic Behavior and Organization, 3
R. Wets (1989)
Stochastic programmingOptimization
M. Rothschild, J. Stiglitz (1970)
Increasing risk: I. A definitionJournal of Economic Theory, 2
I. Karatzas, S. Shreve (2010)
Methods of Mathematical Finance
Lopes, L. Lola (1987)
[Advances in Experimental Social Psychology] Advances in Experimental Social Psychology Volume 20 Volume 20 || Between Hope and Fear: The Psychology of Risk
S. Pliska (1986)
A Stochastic Calculus Model of Continuous Trading: Optimal PortfoliosMath. Oper. Res., 11
A. Cherny, D. Madan (2007)
New Measures for Performance EvaluationCapital Markets: Market Efficiency eJournal
R. Merton (1969)
Lifetime Portfolio Selection under Uncertainty: The Continuous-Time CaseThe Review of Economics and Statistics, 51
Berkelaar (2004)
Optimal Portfolio Choice under Loss AversionRev. Econ. Stat, 86
Thomas Goll, L. Rüschendorf (2001)
Minimax and minimal distance martingale measures and their relationship to portfolio optimizationFinance and Stochastics, 5
H. Föllmer, Peter Leukert (1999)
Quantile hedgingFinance and Stochastics, 3
David Schmeidleis (1989)
SUBJECTIVE PROBABILITY AND EXPECTED UTILITY WITHOUT ADDITIVITY
M. Kulldorff (1993)
Optimal control of favorable games with a time limitSiam Journal on Control and Optimization, 31
M. Yaari (1987)
The Dual Theory of Choice under RiskEconometrica, 55
Kahneman Kahneman, Tversky Tversky (1979)
Prospect Theory: An Analysis of Decision under RiskEconometrica, 47
P. Grigor’ev, Yu. Kan (2004)
Optimal Control of the Investment Portfolio with Respect to the Quantile CriterionAutomation and Remote Control, 65
(2008)
SP/A model in continuous time
Arjan Berkelaar, Roy Kouwenberg, T. Post (2000)
Optimal Portfolio Choice under Loss AversionReview of Economics and Statistics, 86
S. Jacka (1992)
A Martingale Representation Result and an Application to Incomplete Financial MarketsMathematical Finance, 2
R. Merton (1975)
Optimum Consumption and Portfolio Rules in a Continuous-Time Model*
Philip Dybvig (1988)
Distributional Analysis of Portfolio ChoiceThe Journal of Business, 61
W. Schachermayer, M. Sîrbu, E. Taflin (2007)
In which financial markets do mutual fund theorems hold true?Finance and Stochastics, 13
J. Harrison, S. Pliska (1981)
Martingales and stochastic integrals in the theory of continuous tradingStochastic Processes and their Applications, 11
J. Harrison, S. Pliska (1983)
A stochastic calculus model of continuous trading: Complete marketsStochastic Processes and their Applications, 15
Browne (1999)
Reaching Goals by a Deadline: Digital Options and Continuous-time Active Portfolio ManagementAdv. Appl. Probab, 31
H. Föllmer, D. Kramkov (1997)
Optional decompositions under constraintsProbability Theory and Related Fields, 109
S. Browne (1996)
Reaching goals by a deadline: digital options and continuous-time active portfolio managementAdvances in Applied Probability, 31
D. Schmeidler (1989)
Subjective Probability and Expected Utility without AdditivityEconometrica, 57
A. Schied (2004)
On the Neyman–Pearson problem for law-invariant risk measures and robust utility functionalsAnnals of Applied Probability, 14
M. David (1979)
HARRISON, J. Michael, and KREPS, . Martingales and Arbitrage in Multiperiod Securities Markets, Journal of Economic Theory, , ., 20
Dhaene Dhaene, Vanduffel Vanduffel, Goovaerts Goovaerts, Kaas Kaas, Vyncke Vyncke (2005)
Commonotonic Approximations for Optimal Portfolio Selection ProblemsJ. Risk Insur, 72
A. Tversky, D. Kahneman (1992)
Advances in prospect theory: Cumulative representation of uncertaintyJournal of Risk and Uncertainty, 5
A portfolio choice model in continuous time is formulated for both complete and incomplete markets, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as the decision variable. This formulation covers a wide body of existing and new models with law‐invariant preference measures, including expected utility maximization, mean–variance, goal reaching, Yaari's dual model, Lopes' SP/A model, behavioral model under prospect theory, as well as those explicitly involving VaR and CVaR in objectives and/or constraints. A solution scheme to this quantile model is proposed, and then demonstrated by solving analytically the goal‐reaching model and Yaari's dual model. A general property derived for the quantile model is that the optimal terminal payment is anticomonotonic with the pricing kernel (or with the minimal pricing kernel in the case of an incomplete market if the investment opportunity set is deterministic). As a consequence, the mutual fund theorem still holds in a market where rational and irrational agents co‐exist.
Mathematical Finance – Wiley
Published: Apr 1, 2011
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.