Summary
In an incomplete financial market where an investor maximizes the expected constant relative risk aversion utility of his terminal wealth, we present an approximate solution for the optimal portfolio. We take into account a set of assets and a set of state variables, all of them described by general diffusion processes. Finally, we supply an easy test for checking the goodness of the approximate result.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Björk T (1998) Arbitrage Theory in Continuous Time. Oxford University Press, New York.
Boulier JF, Huang SJ, Taillard G (2001) Optimal Management Under Stochastic Interest. Insurance: Mathematics and Economics 28:173–189.
Buckdahn R, Ma J (2001a) Stochastic viscosity solutions for nonlinear stochastic partial differential equations - Part I. Stochastic Processes and their Applications 93:181–204.
Buckdahn R, Ma J (2001b) Stochastic viscosity solutions for nonlinear stochastic partial differential equations - Part II. Stochastic Processes and their Applications 93:205–228.
Campbell JY (2000) Asset Pricing at the Millennium. The Journal of Finance 55:1515–1567.
Chacko G, Viceira LM (2005) Dynamic consumption and portfolio choice with stochastic volatility in incomplete markets. The Review of Financial Study 18:1369–1402.
Cox JC, Huang CF (1989) Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory 49:33–83.
Cox JC, Huang CF (1991) A variational problem arising in financial economics. Journal of Mathematical Economics 20:465–487.
Cox JC, Ingersoll JE Jr., Ross SA (1985) A Theory of the Term Structure of Interest Rates. Econometrica 53:385–407.
Crandall MG, Ishii H, Lions P (1992) User’s guide to viscosity solutions of second order partial differential equations. Bulletin of the American Mathematical Society 27:1–67.
Deelstra G, Grasselli M, Koehl PF (2000) Optimal investment strategies in a CIR framework. Journal of Applied Probability 37:1–12.
. Duffie D (1996) Dynamic Asset Pricing Theory. Second edition, Princeton University Press.
Duffie D, Kan R (1996) A Yield-Factor Model of Interest Rates. Mathematical Finance 6:379–406.
. Freiling G (2002) A survey of nonsymmetric Riccati equations. Linear Algebra and its Applications 351–352:243–270.
. Karatzas I, Shreve SE (1998) Methods of Mathematical Finance. Springer.
Kim TS, Omberg E (1996) Dynamic Nonmyopic Portfolio Behavior. The Review of Financial Studies 9:141–161.
Kogan L, Uppal R (1999) Risk Aversion and Optimal Portfolio Policies in Partial and General Equilibrium Economies. Working Paper, Wharton.
Lioui A, Poncet P (2001) On Optimal Portfolio Choice under Stochastic Interest Rates. Journal of Economic Dynamics and Control 25:1841–1865.
Menoncin F (2002) Optimal Portfolio and Background Risk: An Exact and an Approximated Solution. Insurance: Mathematics and Economics 31:249–265.
Merton RC (1969) Lifetime Portfolio Selection under Uncertainty: the Continuous-Time Case. Review of Economics and Statistics 51:247–257.
Merton RC (1971) Optimum Consumption and Portfolio Rules in a Continuous Time Model. Journal of Economic Theory 3:373–413.
Øksendal B (2000) Stochastic Differential Equations - An Introduction with Applications – Fifth edition. Springer, Berlin.
Vasiček O (1977) An Equilibrium characterization of the Term Structure. Journal of Financial Economics 5:177–188.
Wachter JA (1998) Portfolio and Consumption Decisions Under Mean-Reverting Returns: An Exact Solution for Complete Markets. Working Paper, Harvard University.
. Yong J, Zhou XY (1999) Stochastic Controls - Hamiltonian Systems and HJB Equations. Springer.
Zariphopoulou T (2001) A solution approach to valuation with unhedgeable risks. Finance and Stochastics 5:61–82.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Menoncin, F. (2008). An Approximate Solution for Optimal Portfolio in Incomplete Markets. In: Sarychev, A., Shiryaev, A., Guerra, M., Grossinho, M.d.R. (eds) Mathematical Control Theory and Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69532-5_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-69532-5_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69531-8
Online ISBN: 978-3-540-69532-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)