Numerical Methods for Real Options in Telecommunications

This thesis applies modern financial option valuation methods to the problem of telecommunication network capacity investment decision timing. In particular, given a cluster of base stations (wireless network with a certain traffic capacity per base station), the objective of this thesis is to determine when it is optimal to increase capacity to each of the base stations of the cluster. Based on several time series taken from the wireless and bandwidth industry, it is argued that capacity usage is the major uncertain component in telecommunications. It is found that price has low volatility when compared to capacity usage. A real options approach is then applied to derive a two dimensional partial integro-differential equation (PIDE) to value investments in telecommunication infrastructure when capacity usage is uncertain and has temporary sudden large variations. This real options PIDE presents several numerical challenges. First, the integral term must be solved accurately and quickly enough such that the general PIDE solution is reasonably accurate. To deal with the integral term, an implicit method is suggested. Proofs of timestepping stability and convergence of a fixed point iteration scheme are presented. The correlation integral is computed using a fast Fourier transform (FFT) method. Techniques are developed to avoid wrap-around effects. This method is tested on option pricing problems where the underlying asset follows a jump diffusion process. Second, the absence of diffusion in one direction of the two dimensional PIDE creates numerical challenges regarding accuracy and timestep selection. A semi-Lagrangian method is presented to alleviate these issues. At each timestep, a set of one dimensional PIDEs is solved and the solution of each PIDE is updated using semi-Lagrangian timestepping. Crank-Nicolson and second order backward differencing timestepping schemes are studied. Monotonicity and stability results are derived. This method is tested on continuously observed Asian options. Finally, a five factor algorithm that captures many of the constraints of the wireless network capacity investment decision timing problem is developed. The upgrade decision for different upgrade decision intervals (e. g. monthly, quarterly, etc. ) is studied, and the effect of a safety level (i. e. the maximum allowed capacity used in practice on a daily basis—which differs from the theoretical maximum) is investigated

Impact of age over 75 years on outcomes after pancreaticoduodenectomy.

International audienceBACKGROUND: The risks associated with pancreaticoduodenectomy (PD) in elderly patients continue to be debated. The aim of our study was to assess the incidence of death and postoperative complications following PD and identify the risk factors in patients >75 y. STUDY DESIGN: All patients who underwent PD between January 2000 and September 2009 were analyzed retrospectively. Patients were divided into two groups according to age (Group 1: patients aged 75 y proved to be predictive factors for mortality (OR 11.04, IC95% [2.57; 47.49], P = 0.001). When compared with Group 1, Group 2 was associated with increased postoperative deaths (24.4% versus 3.66%, P < 0.001) and pancreatic fistulas (26.8% versus 13.2%, P = 0.041), in particular, Grade C fistulas (14.6% versus 4.4%, P = 0.023). In multivariate analysis, only PH proved to be an independent predictive factor for mortality (OR 12.9, IC95% [1.07; 155.5], P = 0.04). CONCLUSIONS: PD in elderly patients aged over 75 y appears to be associated with an increased risk of postoperative death and pancreatic fistula. No single preoperative factor made it possible to predict this risk