All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 69

Showing per page

Robust portfolio selection under exponential preferences

Dariusz Zawisza (2010)

Applicationes Mathematicae

We consider an incomplete market with an untradable stochastic factor and a robust investment problem based on the CARA utility. We formulate it as a stochastic differential game problem, and use Hamilton-Jacobi-Bellman-Isaacs equations to derive an explicit representation of the robust optimal portfolio; the HJBI equation is transformed using a substitution of the Cole-Hopf type. Not only the pure investment problem, but also a problem of robust hedging is taken into account: an agent tries to...

Smooth solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems to be the...

Smooth Solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear Hamiltonian seems to be...

Stochastic differential games involving impulse controls

Feng Zhang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.

Stochastic differential games involving impulse controls*

Feng Zhang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.

Target achieving portfolio under model misspecification: quadratic optimization framework

Dariusz Zawisza (2012)

Applicationes Mathematicae

We incorporate model uncertainty into a quadratic portfolio optimization framework. We consider an incomplete continuous time market with a non-tradable stochastic factor. Two stochastic game problems are formulated and solved using Hamilton-Jacobi-Bellman-Isaacs equations. The proof of existence and uniqueness of a solution to the resulting semilinear PDE is also provided. The latter can be used to extend many portfolio optimization results.

Viscosity solutions of the Isaacs equation οn an attainable set

Leszek Zaremba (1994)

Applicationes Mathematicae

We apply a modification of the viscosity solution concept introduced in [8] to the Isaacs equation defined on the set attainable from a given set of initial conditions. We extend the notion of a lower strategy introduced by us in [17] to a more general setting to prove that the lower and upper values of a differential game are subsolutions (resp. supersolutions) in our sense to the upper (resp. lower) Isaacs equation of the differential game. Our basic restriction is that the variable duration time...

Weak infinitesimal operators and stochastic differential games.

Ramón Ardanuy, A. Alcalá (1992)

Stochastica

This article considers the problem of finding the optimal strategies in stochastic differential games with two players, using the weak infinitesimal operator of process xi the solution of d(xi) = f(xi,t,u1,u2)dt + sigma(xi,t,u1,u2)dW. For two-person zero-sum stochastic games we formulate the minimax solution; analogously, we perform the solution for coordination and non-cooperative stochastic differential games.

Currently displaying 41 – 60 of 69