In this article we propose a $\alpha$-hypergeometric model with uncertain volatility (UV) where derive worst-case scenario for option pricing. The approach is based on the connexion between certain class of nonlinear partial differential equations HJB-type (G-HJB equations), that govern expectation UV and provide an alternative to difficult calibration problem models, second-order backward stoc...

This paper treats a finite time horizon optimal control problem in which the controlled state dynamics is governed by a general system of stochastic functional differential equations with a bounded memory. An infinite-dimensional HJB equation is derived using a Bellman-type dynamic programming principle. It is shown that the value function is the unique viscosity solution of the HJB equation. I...

1 We present efficient partial differential equation (PDE) methods for continuous time mean2 variance portfolio allocation problems when the underlying risky asset follows a stochastic 3 volatility process. The standard formulation for mean variance optimal portfolio allocation 4 problems gives rise to a two-dimensional non-linear Hamilton-Jacobi-Bellman (HJB) PDE. We 5 use a wide stencil metho...

Abstract In this paper, we consider the stochastic optimal control problem for jump-diffusion models with state constraints. general, value function of such problems is discontinuous viscosity solution associated Hamilton-Jacobi-Bellman (HJB) equation since regularity cannot be guaranteed at boundary constraint. By adapting target theory, obtain an equivalent representation original by means ba...

The usual framework of control is the one given in probably the most studied control problem, stochastic regulator control problem, which deals with minimizing a performance index of a system governed by a set of differential equations. The stochastic linear regulator problem has been studied by many authors including Bensoussan [4], Fleming and Soner [9] for nondegenerate diffusions. Da Prato ...

5 We present efficient partial differential equation (PDE) methods for continuous time mean6 variance portfolio allocation problems when the underlying risky asset follows a jump-diffusion. 7 The standard formulation of mean-variance optimal portfolio allocation problems, where the 8 total wealth is the underlying stochastic process, gives rise to a one-dimensional (1-D) non-linear 9 Hamilton-J...

This paper is concerned with Sobolev weak solution of Hamilton-Jacobi-Bellman (HJB) equation. This equation is derived from the dynamic programming principle in the study of the stochastic optimal control problem. Adopting Doob-Meyer decomposition theorem as one of main tool, we prove that the optimal value function is the unique Sobolev weak solution of the corresponding HJB equation. For the ...

We study a class of optimal control problems with state constraint, where the state equation is a differential equation with delays in the control variable. This class of problems arises in some economic applications, in particular in optimal advertising problems. The optimal control problem is embedded in a suitable Hilbert space, and the associated Hamilton–Jacobi–Bellman (HJB) equation is co...