How to provide access to next generation networks? The effect of risk allocation on investment and cooperation incentives

This paper analyzes the incentives to invest in Next Generation Access Networks (NGA) in a framework with horizontal product differentiation with price competition between an investing and an access seeking firm. Given uncertainty about the success of the NGA, I compare regulatory regimes with symmetric and with asymmetric risk allocation to the firms having the opportunity to cooperate and jointly roll-out the NGA. I find that private incentives to cooperate might coincide with the consumer surplus maximizing outcome. Whether the firms realize this socially desirable outcome depends on the outside option, i.e. the implemented access regime. The optimal regulatory policy is not only subject to the probability that the NGA succeed but depends even more on the degree of product differentiation in the retail market. Therefore, the implementation of different access regimes subject to the degree of product differentiation seems favorable. For heterogeneous retail products, an asymmetric risk allocation not only increases the chances of cooperation but lowers the risk of overinvestment. For homogeneous goods, a symmetric risk allocation is superior as it ensures sufficient investment incentives even if competition is very intensive.Next Generation Access Networks, investment, access regulation, cooperation

Time discretization and Markovian iteration for coupled FBSDEs

In this paper we lay the foundation for a numerical algorithm to simulate high-dimensional coupled FBSDEs under weak coupling or monotonicity conditions. In particular, we prove convergence of a time discretization and a Markovian iteration. The iteration differs from standard Picard iterations for FBSDEs in that the dimension of the underlying Markovian process does not increase with the number of iterations. This feature seems to be indispensable for an efficient iterative scheme from a numerical point of view. We finally suggest a fully explicit numerical algorithm and present some numerical examples with up to 10-dimensional state space.Comment: Published in at http://dx.doi.org/10.1214/07-AAP448 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stochastic calculus for convoluted L\'{e}vy processes

We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation L\'{e}vy process with a Volterra-type kernel. This class of processes contains, for example, fractional L\'{e}vy processes as studied by Marquardt [Bernoulli 12 (2006) 1090--1126.] The integral which we introduce is a Skorokhod integral. Nonetheless, we avoid the technicalities from Malliavin calculus and white noise analysis and give an elementary definition based on expectations under change of measure. As a main result, we derive an It\^{o} formula which separates the different contributions from the memory due to the convolution and from the jumps.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ115 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A primal-dual algorithm for BSDEs

We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dynamic program, which was pre-computed, e.g., by least-squares Monte Carlo, our methodology allows to construct a confidence interval for the unknown true solution of the time discretized (reflected) BSDE at time 0. We numerically demonstrate the practical applicability of our method in two five-dimensional nonlinear pricing problems where tight price bounds were previously unavailable

Maximal inequalities for fractional L\'evy and related processes

In this paper we study processes which are constructed by a convolution of a deterministic kernel with a martingale. A special emphasis is put on the case where the driving martingale is a centred L\'evy process, which covers the popular class of fractional L\'evy processes. As a main result we show that, under appropriate assumptions on the kernel and the martingale, the maximum process of the corresponding `convoluted martingale' is $p$-integrable and we derive maximal inequalities in terms of the kernel and of the moments of the driving martingale

Finite Variation of Fractional Levy Processes

Various characterizations for fractional Levy process to be of finite variation are obtained, one of which is in terms of the characteristic triplet of the driving Levy process, while others are in terms of differentiability properties of the sample paths. A zero-one law and a formula for the expected total variation is also given.Comment: to appear in Journal of Theoretical Probabilit