We introduce stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. The fractional derivative is approximated in each sub domain using orthogonal polynomials and stability of the scheme is achieved through weakly imposed boundary and interface conditions by using a penalty term. We discuss accuracy an...

In this paper, we consider the surplus process of the classical continuous time risk model containing an independent diffusion (Wiener) process. We generalize the defective renewal equation for the expected discounted function of a penalty at the time of ruin in Garber and Landry [Insurance: Math. Econ. 22 (1998) 263]. Then an asymptotic formula for the expected discounted penalty function is p...

In this paper, we derive the optimal boundary for pair trading. This boundary defines the points of entry into or exit from the market for a given stock pair. However, if the assumed model contains uncertainty, the resulting boundary could result in large losses. To avoid this, we develop a more robust strategy by accounting for the model uncertainty. To incorporate the model uncertainty, we us...

where the functions ρ, u, θ and d represent the mass density,the velocity field, the absolute temperature and the unit vector field that represents the macroscopic molecular orientation of the liquid crystal material. P stands for the pressure, S denotes the viscous stress tensor. The positive constants ν, κ denote the competition between kinetic energy and potential energy, and microscopic ela...

In this paper, we propose an algorithm based on Fletcher’s Sl1QP method and the trust region technique for solving Nonlinear Second-Order Cone Programming (NSOCP) problems. The Sl1QP method was originally developed for nonlinear optimization problems with inequality constraints. It converts a constrained optimization problem into an unconstrained problem by using the l1 exact penalty function, ...

Penalty approaches can be used to efficiently resolve collisions of dynamically simulated rigid and deformable objects. These approaches compute penalty forces based on the penetration depth of intersecting objects and there exist many algorithms for estimating the exact penetration depth. However, in discrete-time simulations, this information can cause non-plausible collision responses in cas...

For constrained nonsmooth optimization problems, continuously diierentiable penalty functions and barrier functions are given. They are proved exact in the sense that under some nondegeneracy assumption, local optimizers of a nonlinear program are also optimizers of the associated penalty or barrier function. This is achieved by augmenting the dimension of the program by a variable that control...