Covering theory for complexes of groups

We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and isometry of universal covers. We characterize faithful complexes of groups and prove a conjugacy theorem for groups acting freely on polyhedral complexes. We also define an equivalence relation on coverings of complexes of groups, which allows us to construct a bijection between such equivalence classes, and subgroups or overgroups of a fixed lattice $\Gamma$ in the automorphism group of a locally finite polyhedral complex $X$.Comment: 47 pages, 1 figure. Comprises Sections 1-4 of previous submission. New introduction. To appear in J. Pure Appl. Algebr

A decomposition approach for the discrete-time approximation of BSDEs with a jump II: the quadratic case

We study the discrete-time approximation for solutions of quadratic forward back- ward stochastic differential equations (FBSDEs) driven by a Brownian motion and a jump process which could be dependent. Assuming that the generator has a quadratic growth w.r.t. the variable z and the terminal condition is bounded, we prove the convergence of the scheme when the number of time steps n goes to infinity. Our approach is based on the companion paper [15] and allows to get a convergence rate similar to that of schemes of Brownian FBSDEs

Progressive enlargement of filtrations and Backward SDEs with jumps

This work deals with backward stochastic differential equation (BSDE) with random marked jumps, and their applications to default risk. We show that these BSDEs are linked with Brownian BSDEs through the decomposition of processes with respect to the progressive enlargement of filtrations. We show that the equations have solutions if the associated Brownian BSDEs have solutions. We also provide a uniqueness theorem for BSDEs with jumps by giving a comparison theorem based on the comparison for Brownian BSDEs. We give in particular some results for quadratic BDSEs. As applications, we study the pricing and the hedging of a European option in a complete market with a single jump, and the utility maximization problem in an incomplete market with a finite number of jumps

A decomposition approach for the discrete-time approximation of FBSDEs with a jump I : the Lipschitz case

We study the discrete-time approximation for solutions of forward-backward stochas- tic dierential equations (FBSDEs) with a jump. In this part, we study the case of Lipschitz generators, and we refer to the second part of this work [15] for the quadratic case. Our method is based on a result given in the companion paper [14] which allows to link a FBSDE with a jump with a recursive system of Brownian FBSDEs. Then we use the classical results on discretization of Brownian FBSDEs to approximate the recursive system of FBSDEs and we recombine these approximations to get a dis- cretization of the FBSDE with a jump. This approach allows to get a convergence rate similar to that of schemes for Brownian FBSDEs

Mean-Variance Hedging on uncertain time horizon in a market with a jump

In this work, we study the problem of mean-variance hedging with a random horizon T ^ tau, where T is a deterministic constant and is a jump time of the underlying asset price process. We rst formulate this problem as a stochastic control problem and relate it to a system of BSDEs with jumps. We then provide a veri cation theorem which gives the optimal strategy for the mean-variance hedging using the solution of the previous system of BSDEs. Finally, we prove that this system of BSDEs admits a solution via a decomposition approach coming from ltration enlargement theory

Application Research of 3D Printing Technology on Dress Forms

Abstract— Dress form is an essential tool in the clothing-making process for pattern block development, draping and quality inspection. However, it is noted that a single dress form is not applicable for a large variety body shapes. There are adjustable dress forms and custom-made dress forms to attempt to make up for the insufficiency of conventional dress forms. However, such types of dress forms are rather costly and their effectiveness is debatable. With this is mind, a customised adjustable kit for the dress form was developed, with the aim to cover different sizes and shapes more precisely. The kit adopts 3D printing technology which enables generating and changing the shape of components efficiently