Optimal scheduling of material handling devices in a PCB production line: problem formulation and a polynomial algorithm.
Optimal state estimation of a Markov process from point process observations
Optimal stopping and impulsive control of one-dimensional diffusion processes
Optimal stopping with advanced information flow: selected examples
We study optimal stopping problems for some functionals of Brownian motion in the case when the decision whether or not to stop before (or at) time t is allowed to be based on the δ-advanced information , where is the σ-algebra generated by Brownian motion up to time s, s ≥ -δ, δ > 0 being a fixed constant. Our approach involves the forward integral and the Malliavin calculus for Brownian motion.
Optimization of consumption with partial observation-Jensen inequality method
A solution to a model of optimal consumption with partial observation considered in [LOS] is presented. The approach is based on the Jensen inequality and does not require application of the filtering equation.
Optimization of Discrete-Time, Stochastic Systems
* This research was supported by a grant from the Greek Ministry of Industry and Technology.In this paper we study discrete-time, finite horizon stochastic systems with multivalued dynamics and obtain a necessary and sufficient condition for optimality using the dynamic programming method. Then we examine a nonlinear stochastic discrete-time system with feedback control constraints and for it, we derive a necessary and sufficient condition for optimality which we then use to establish the existence...
Option pricing in a CEV model with liquidity costs
The goal of this paper is to make an attempt to generalise the model of pricing European options with an illiquid underlying asset considered by Rogers and Singh (2010). We assume that an investor's decisions have only a temporary effect on the price, which is proportional to the square of the change of the number of asset units in the investor's portfolio. We also assume that the underlying asset price follows a CEV model. To prove existence and uniqueness of the solution, we use techniques similar...
Option pricing in a regime-switching model using the fast Fourier transform.
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Oscillation and non-oscillation in solutions of nonlinear stochastic delay differential equations.
-variation for families of local times on lines
Parabolic SPDEs degenerating on the boundary of nonsmooth domain.
Parabolic variational inequalities with generalized reflecting directions
We study, in a Hilbert framework, some abstract parabolic variational inequalities, governed by reflecting subgradients with multiplicative perturbation, of the following type: y´(t)+ Ay(t)+0.t Θ(t,y(t)) ∂φ(y(t))∋f(t,y(t)),y(0) = y0,t ∈[0,T] where A is a linear self-adjoint operator, ∂φ is the subdifferential operator of a proper lower semicontinuous convex function φ defined on a suitable Hilbert space, and Θ is the perturbing term which acts on the set of reflecting directions, destroying the...
Parametric dependence of the solution processes on the coefficients in McShane's stochastic integral equation systems
Parametric inference for mixed models defined by stochastic differential equations
Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned...
Partially observed optimal controls of forward-backward doubly stochastic systems
The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied to study a partially-observed...
Partition-dependent stochastic measures and -deformed cumulants.
Path properties of a class of locally asymptotically self similar processes.
Pathwise differentiability for SDEs in a convex polyhedron with oblique reflection
In this paper, the object of study is a Skorohod SDE in a convex polyhedron with oblique reflection at the boundary. We prove that the solution is pathwise differentiable with respect to its deterministic starting point up to the time when two of the faces are hit simultaneously. The resulting derivatives evolve according to an ordinary differential equation, when the process is in the interior of the polyhedron, and they are projected to the tangent space, when the process hits the boundary, while...