We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach. Our proof follows from Gosper’s algorithm. The binomial model as heralded by Cox et al. (1979), has become a well-known approa...

Our general concern is with how to integrate a representation of action into an existing set of state constraints. As has been observed in the literature, state constraints implicitly define indirect effects of actions as well as indirectly imposing further preconditions on the performance of actions. Thus, any representation scheme we propose must address the ramification and qualification pro...

This paper presents a closed-form solution to the inverse kinematic problem for general fluoroscopic C-arms. The resulting algorithm determines the necessary joint parameters for imaging a given point of interest p from a given direction z. The existence and uniqueness of the solution is proven for all p and z. The inverse kinematics lays the basis for a completely robotized C-arm. The paper de...

In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an I...

Monocular depth has been found using estimation, closed-form solution and learning techniques. Estimation and closed-form solution compute the depth from motion, while learning techniques calculate the depth using a single image with a depth map as a supervisor. This paper presents a new closed form solution for monocular depth from motion. The proposed method builds on the notation that an int...

Photorealistic image style transfer algorithms aim at stylizing a content photo using the style of a reference photo with the constraint that the stylized photo should remains photorealistic. While several methods exist for this task, they tend to generate spatially inconsistent stylizations with noticeable artifacts. In addition, these methods are computationally expensive, requiring several m...

In this report, we present the analysis of a 6 DOF robot end-effector built to study telerobotic assembly of NASA hardwares in space. Since the end-efector is required to perform high precision motion in a limited workspace, closed-kinematic chain mechanism is chosen for its design. A closed-form solution is obtained for the inverse kinematic problem and an itemtive pmedure employing Newton-Rap...

The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...

Electro-magneto-thermo-elastic response of a thick double-layered cylinder made from a homogeneous interlayer and a functionally graded piezoelectric material (FGPM) outer layer is investigated. Material properties of the FGPM layer vary along radius based on the power law distribution. The vessel is subjected to an internal pressure, an induced electric potential, a uniform magnetic field and ...

This paper presents a novel procedure for solving the equations system of the rotating crack model used for reinforced concrete. It is implemented in the programme NonOPt where it is used to optimise the reinforcement design of D regions. The procedure is based on solving explicit closed-form relations without the need to incrementally increase the applied loads. The solution procedure is based...