Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/viscosity-solutions-of-an-infinite-dimensional-black-scholes-9mW40yQe2g
References (45)
-
Fausto Gozzi, E. Rouy (1996)
Regular Solutions of Second-Order Stationary Hamilton-Jacobi EquationsJournal of Differential Equations, 130
-
(1993)
Świȩch, On partial sup-convolutions, a lemma of P.L. Lions and viscosity solutions in Hilbert spaces -
P. Cannarsa, G. Prato (1991)
Second-order Hamilton-Jacobi equations in infinite dimensionsSiam Journal on Control and Optimization, 29
-
S. Romagnoli, Tiziano Vargiolu (2000)
Robustness of the Black-Scholes approach in the case of options on several assetsFinance and Stochastics, 4
-
Fausto Gozzi, Tiziano Vargiolu (2002)
Superreplication of European multiasset derivatives with bounded stochastic volatilityMathematical Methods of Operations Research, 55
-
M. Nisio (1998)
On infinite-dimensional stochastic differential gamesOsaka Journal of Mathematics, 35
-
N. Karoui, M. Jeanblanc-Picqué, S. Shreve (1998)
Robustness of the Black and Scholes FormulaMathematical Finance, 8
-
V. Barbu, G. Prato (1983)
Hamilton-Jacobi equations in Hilbert spaces -
(1983)
Semigroups of Linear Operators and Applications to Partial Differential Equations -
M. Crandall, P. Lions (1990)
Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. IV: Hamiltonians with unbounded linear termsJournal of Functional Analysis, 90
-
Tiziano Vargiolu (1999)
Invariant measures for the Musiela equation with deterministic diffusion termFinance and Stochastics, 3
-
M. Nisio (1999)
On value function of stochastic differential games in infinite dimensions and its application to sensitive controlOsaka Journal of Mathematics, 36
-
S. Cerrai, Fausto Gozzi (1995)
Strong solutions of Cauchy problems associated to weakly continuous semigroupsDifferential and Integral Equations
-
Fausto Gozzi, E. Rouy, A. Swiech (2000)
Second Order Hamilton--Jacobi Equations in Hilbert Spaces and Stochastic Boundary ControlSIAM J. Control. Optim., 38
-
M. Crandall, P. Lions (1991)
Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. V. Unbounded linear terms and B-continuous solutionsJournal of Functional Analysis, 97
-
W. Fleming, H. Soner, H. Soner, Div Mathematics, Florence Fleming, Serpil Soner (1992)
Controlled Markov processes and viscosity solutions -
(1997)
Finite dimensional approximations for the Musiela model in the Gaussian case -
J. Yong, X. Zhou (1999)
Stochastic Controls: Hamiltonian Systems and HJB Equations -
Fausto Gozzi (1995)
Regularity of solutions of a second order hamilton-jacobi equation and application to a control problemCommunications in Partial Differential Equations, 20
-
M. Avellaneda, Arnon Levy, Antonio Par (1995)
Pricing and hedging derivative securities in markets with uncertain volatilitiesApplied Mathematical Finance, 2
-
Fausto Gozzi, Tiziano Vargiolu (2002)
On the superreplication approach for european multiasset derivatives. -
B. Goldys, M. Musiela (1996)
On Partial Differential Equations Related To Term Structure Models -
C. Stegall (1978)
Optimization of functions on certain subsets of Banach spacesMathematische Annalen, 236
-
M. Crandall, P. Lions (1983)
Viscosity solutions of Hamilton-Jacobi equationsTransactions of the American Mathematical Society, 277
-
M. Crandall, H. Ishii, P. Lions (1992)
User’s guide to viscosity solutions of second order partial differential equationsBulletin of the American Mathematical Society, 27
-
N. Karoui, J. Rochet (1995)
CHANGES OF NUMERAIRE, CHANGES OF PROBABILITY MEASURE -
M. Musiela, M. Rutkowski (2002)
Martingale Methods in Financial Modelling -
B. Goldys, M. Musiela, D. Sondermann (2000)
Lognormality of rates and term structure modelsStochastic Analysis and Applications, 18
-
G. Prato (1985)
Some Results on Bellman Equation in Hilbert SpacesSiam Journal on Control and Optimization, 23
-
(1992)
Direct solution of a second order Hamilton-Jacobi equation in Hilbert spaces, Stochastic partial differential equations and applications, G -
(1992)
On partial sup - convolutions , a lemma of P . L . Lions and viscosity solutions in Hilbert spaces -
H. Ishii (1993)
Viscosity solutions of nonlinear second-order partial differential equations in hilbert spacesCommunications in Partial Differential Equations, 18
-
(1993)
Stochastic PDEs and term structure models, Journees Internationales de Finance, IGR-AFFI -
P. Lions (1989)
Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation -
(1998)
Bellman’s inclusions and excessive measures, preprint no -
M. Renardy (1995)
Polar decomposition of positive operators and a problem of crandall and lionsApplicable Analysis, 57
-
(1992)
Lions, User’s guide to viscosity solutions of second order partial differential equations -
D. Gatarek, A. Swiech (1999)
Optimal stopping in Hilbert spaces and pricing of American optionsMathematical Methods of Operations Research, 50
-
Terry Lyons (1995)
Uncertain volatility and the risk-free synthesis of derivativesApplied Mathematical Finance, 2
-
Fausto Gozzi, Tiziano Vargiolu (2002)
On the Superreplication Approach for European Interest Rates Derivatives -
(1991)
Direct solution of a second order Hamilton - Jacobi equation in Hilbert spaces , Stochastic partial differential equations and applications -
P. Cannarsa, G. Daprato (1993)
On a functional analysis approach to parabolic equations in infinite dimensionsJournal of Functional Analysis, 118
-
(1992)
Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and its Applications -
Fausto Gozzi, A. Swiech (2000)
Hamilton–Jacobi–Bellman Equations for the Optimal Control of the Duncan–Mortensen–Zakai Equation☆☆☆Journal of Functional Analysis, 172
-
M. Crandall (1994)
Viscosity Solutions of Fully Nonlinear Equations
- Publisher
- Springer Journals
- Copyright
- Copyright © Inc. by 2003 Springer-Verlag New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-003-0764-8
- Publisher site
- See Article on Publisher Site
Abstract
We study an infinite-dimensional Black—Scholes—Barenblatt equation which is a Hamilton—Jacobi—Bellman equation that is related to option pricing in the Musiela model of interest rate dynamics. We prove the existence and uniqueness of viscosity solutions of the Black—Scholes—Barenblatt equation and discuss their stochastic optimal control interpretation. We also show that in some cases the solution can be locally uniformly approximated by solutions of suitable finite-dimensional Hamilton—Jacobi—Bellman equations.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: May 21, 2003