Access the full text.
Sign up today, get DeepDyve free for 14 days.
G. Kallianpur, R. Karandikar (1999)
Introduction to option pricing theory
D. Duffie, W. Fleming, H. Soner, T. Zariphopoulou (1997)
Hedging in incomplete markets with HARA utilityJournal of Economic Dynamics and Control, 21
I. Karatzas, J. Lehoczky, S. Shreve (1987)
Optimal portfolio and consumption decisions for a “small investor” on a finite horizonSiam Journal on Control and Optimization, 25
W. Fleming, R. Rishel (1975)
Deterministic and Stochastic Optimal Control
O. Ladyženskaja (1968)
Linear and Quasilinear Equations of Parabolic Type, 23
I. Karatzas, J. Lehoczky, S. Sethi, S. Shreve (1986)
Explicit Solution of a General Consumption/Investment ProblemCorporate Finance: Valuation
W. Fleming, T. Zariphopoulou (1991)
An Optimal Investment/Consumption Model with BorrowingMath. Oper. Res., 16
W. Fleming, H. Soner, H. Soner, Div Mathematics, Florence Fleming, Serpil Soner (1992)
Controlled Markov processes and viscosity solutions
T. Zariphopoulou (1991)
Consumption-investment models with constraints[1991] Proceedings of the 30th IEEE Conference on Decision and Control
W. Fleming (1977)
Exit probabilities and optimal stochastic controlApplied Mathematics and Optimization, 4
J. Cox, Chi-Fu Huang (1989)
Optimal consumption and portfolio policies when asset prices follow a diffusion processJournal of Economic Theory, 49
J. Hull, Alan White (1987)
The Pricing of Options on Assets with Stochastic VolatilitiesJournal of Finance, 42
R. Merton (1971)
Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3
T. Zariphopoulou (2001)
A solution approach to valuation with unhedgeable risksFinance and Stochastics, 5
Louis Scott (1987)
Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an ApplicationJournal of Financial and Quantitative Analysis, 22
Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.
Applied Mathematics and Optimization – Springer Journals
Published: Oct 1, 2002
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.