36 research outputs found
Sufficient stochastic maximum principle in a regime-switching diffusion model
We prove a sufficient stochastic maximum principle for the optimal control of
a regime-switching diffusion model. We show the connection to dynamic
programming and we apply the result to a quadratic loss minimization problem,
which can be used to solve a mean-variance portfolio selection problem
Almost sure convergence of a semidiscrete Milstein scheme for SPDE's of Zakai type
A semidiscrete Milstein scheme for stochastic partial differential equations of Zakai type on a bounded domain of R^d is derived. It is shown that the order of convergence of this scheme is 1 for convergence in mean square sense. For almost sure convergence the order of convergence is proved to be 1 - e for any e > 0
An Optimization Approach to Weak Approximation of Lévy-Driven Stochastic Differential Equations
We propose an optimization approach to weak approximation of Lévy-driven stochastic differential equations. We employ a mathematical programming framework to obtain numerically upper and lower bound estimates of the target expectation, where the optimization procedure ends up with a polynomial programming problem. An advantage of our approach is that all we need is a closed form of the Lévy measure, not the exact simulation knowledge of the increments or of a shot noise representation for the time discretization approximation. We also investigate methods for approximation at some different intermediate time points simultaneously
Well-posedness of the transport equation by stochastic perturbation
We consider the linear transport equation with a globally Holder continuous
and bounded vector field. While this deterministic PDE may not be well-posed,
we prove that a multiplicative stochastic perturbation of Brownian type is
enough to render the equation well-posed. This seems to be the first explicit
example of partial differential equation that become well-posed under the
influece of noise. The key tool is a differentiable stochastic flow constructed
and analysed by means of a special transformation of the drift of Ito-Tanaka
type.Comment: Addition of new part
Unique strong solutions of Lévy processes driven stochastic differential equations with discontinuous coefficients
An optimization approach to weak approximation of Lévy-driven stochastic differential equations with application to option pricing
We propose an optimization approach to weak
approximation of Lévy-driven stochastic differential equations.
We employ a mathematical programming framework to obtain
numerically upper and lower bound estimates of the target
expectation, where the optimization procedure ends up with
a polynomial programming problem. An advantage of our
approach is that all we need is a closed form of the Lévy
measure, not the exact simulation knowledge of the increments
or of a shot noise representation for the time discretization
approximation. We also investigate methods for approximation
at some different intermediate time points simultaneously