Pricing fuzzy vulnerable options and risk management

The assumption of unrealistic “identical rationality” in classic option pricing theory is released in this article to amend Klein’s [Klein, P. (1996). Pricing Black–Scholes options with correlated credit risk. Journal of Banking Finance, 1211–1129] vulnerable option pricing formula. Through this formula, default risk and liquidity risk are both well-explained when the investment behaviors and market expectations of the participants are heterogeneous. The numerical results show that when the investing decisions of each market participant come from their individual rationality and use their own subjective price to trade, the option price becomes a boundary. The upper boundary becomes an absolutely safe line and the lower boundary becomes an absolutely unsafe line for investors who want to invest in some financial securities with default risk. The proposed model suggests a more realistic pricing mechanism for the issuers and traders who want to value options with default risk.     

On pricing algorithms for batched content delivery systems

Businesses offering video-on-demand (VoD) and downloadable-CD sales are growing in the Internet. Batching of requests coupled with a one-to-many delivery mechanism such as multicast can increase scalability and efficiency. There is very little insight into pricing such services in a manner that utilizes network and system resources efficiently while also maximizing the expectation of revenue. In this paper, we investigate simple, yet effective mechanisms to price content in a batching context. We observe that if customer behavior is well understood and temporally invariant, a fixed pricing scheme can maximize expectation of revenue if there are infinite resources. However, with constrained resources and potentially unknown customer behavior, only a dynamic pricing algorithm can maximize expectation of revenue. We formulate the problem of pricing as a constrained optimization problem and show that maximizing the expectation of revenue can be intractable even when the customer behavior is well known. Since customer behavior is unlikely to be well known in an Internet setting, we develop a model to understand customer behavior online and a pricing algorithm based on this model. Using simulations, we characterize the performance of this algorithm and other simple and deployable pricing schemes under different customer behavior and system load profiles. Based on our work, we propose a pricing scheme that combines the best features of the different pricing schemes and analyze its performance.     

Internet Service Pricing: Flat or Volume?

In this paper, we study the pricing of Internet services under monopoly and duopoly environments using an analytic model in which a service provider and users try to maximize their respective payoffs. We compare a few popular pricing schemes, including flat, volume-based, two-part, and nonlinear tariffs, with respect to revenue, social welfare, and user surplus. We perform a study of the sensitivity of these schemes to the estimation errors. In the duopoly situation, we formulate a simple normal form game between two service providers and study their equilibrium behaviors. Our main findings include: (1) the flat pricing generates higher revenue than the pure volume pricing when the elasticity of demand is low; (2) the volume-based pricing is better for society and users than the flat pricing regardless of the elasticity; (3) the market is segmented into two when one provider provides flat pricing and another provides volume based pricing.     

On a Hopfield Net Arising in the Modelling and Control of Over-Saturated Signalized Intersections

We present a neural method – based on the Hopfield net – for the modelling and control of over-saturated signalized intersections. The problem is to look, in real-time, for lights signal setting which minimize a given traffic criterion such as waiting time. The use of the Hopfield model is straightforward justified by its optimization capabilities, especially its fast time computing (by its own dynamic), which is of a great interest in real-time problems like the traffic control one. The original Hopfield algorithm is modified to take into account proper constraints of the traffic problem. This approach is illustrated by numerical examples of traffic conditions generated by a simulator. We extend the method to urban nets of several interconnected intersections.     

Bicriteria approximation algorithms for scheduling problems with communications delays

We study the problem of simultaneously minimizing the makespan and the average weighted completion time for the precedence multiprocessor constrained scheduling problem with unit execution times and unit communication delays, known as the UET–UCT problem (Munier and König, Operations Research, 45(1), 145–148 (1997)). We propose a simple (16/9, 16/9)-approximation algorithm for the problem with an unrestricted number of machines. We improve our algorithm by adapting a technique first introduced by Aslam et al. (Proceedings of ACM-SODA, pp. 846–847, 1999) and provide a (1.745, 1.745)-approximate solution. For the considered scheduling problem, we prove the existence of a (1.445, 1.445)-approximate solution, improving the generic existence result of Aslam et al. (Proceedings of ACM-SODA, pp. 846–847, 1999). Also notice that our results for the case of an unrestricted number of processors hold for the more general scheduling problem with small communication delays (SCT problem), and for two other classical optimality criteria: maximum lateness and weighted lateness. Finally, we propose an approximation algorithm for the UET–UCT problem with a restricted number of processors.Research partially supported by the thematic network APPOL II (IST 2001-32007) of the European Union, the ACI-GRID2 project of the French government, and the MULT-APPROX project of the France-Berkeley Fund.     

Exploring Traffic Pricing for the Virtual Private Network

This paper explores the implementation issues of network traffic pricing in Internet-based virtual Private Networks (VPNs). A simplified VPN traffic-pricing formula is derived for optimizing VPN bandwidth service welfare. We provide price formulae for both prioritized first-in-first-out bandwidth scheduling and non-prioritized round-robin bandwidth scheduling. A transaction-level pricing architecture based on proxy server technology is proposed, and a prototype traffic-pricing system, VPN Traffic-Pricing Experiment System (VTPES), has been developed to test the transaction-level pricing architecture and examine the pricing formula. Experiments conducted with VTPES show that the pricing mechanism can effectively improve a VPN's transmission efficiency.     

Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems

In this paper we present numerical investigations of four different formulations of the discontinuous Galerkin method for diffusion problems. Our focus is to determine, through numerical experimentation, practical guidelines as to which numerical flux choice should be used when applying discontinuous Galerkin methods to such problems. We examine first an inconsistent and weakly unstable scheme analyzed in Zhang and Shu, Math. Models Meth. Appl. Sci. (M ³ AS) 13, 395–413 (2003), and then proceed to examine three consistent and stable schemes: the Bassi–Rebay scheme (J. Comput. Phys. 131, 267 (1997)), the local discontinuous Galerkin scheme (SIAM J. Numer. Anal. 35, 2440–2463 (1998)) and the Baumann–Oden scheme (Comput. Math. Appl. Mech. Eng. 175, 311–341 (1999)). For an one-dimensional model problem, we examine the stencil width, h-convergence properties, p-convergence properties, eigenspectra and system conditioning when different flux choices are applied. We also examine the ramifications of adding stabilization to these schemes. We conclude by providing the pros and cons of the different flux choices based upon our numerical experiments.This revised version was published online in July 2005 with corrected volume and issue numbers.     

Space–Time Block Coding for Channels with Intersymbol Interference

Stoica, P., and Lindskog, E., Space–Time Block Coding for Channels with Intersymbol Interference, Digital Signal Processing12 (2002) 616–627The downlink of many wireless communication systems can be a MISO channel. An important problem for a MISO channel is how to code across space and time to obtain the same ML receiver as for the corresponding SIMO channel. For flat fading channels, space–time block coding (STBC) is a recent breakthrough solution to this problem. In Lindskog and Paulraj (in Proceedings of ICC'2000, NewOrleans, LA, June 18–22, 2000), STBC has been generalized to channels with intersymbol interference (ISI) for the case of two transmit antennas and one receive antenna. In this paper we first revisit the generalized STBC scheme of Lindskog and Paulraj and show that it has the same appealing properties as the standard STBC for flat fading channels. Then we go on to present an extension of this scheme to ISI channels with any number of transmit and receive antennas.     

A branch and price algorithm for the SS/TDMA problem with cardinality constraint

In this paper, we consider a square n×n traffic matrix D   and a satellite having l≤n$l\le n$ receiving and transmitting antennas. Transmissions are allowed by interconnecting pairs of receiving–transmitting antennas, through an on-board switch. We also assume that no preemption of the communications is allowed, and that changing the configuration of the switch requires a negligible time. We ask for a set of switch configurations that minimizes the total time occurring for transmitting the entire traffic matrix. In the literature, an exact method has been already proposed for the SS/TDMA optimization problem without cardinality constraint (i.e. for instances having l=n), but only heuristics have been proposed for the general case. In this paper, from a known MILP formulation we derive an extended formulation, and we use a column generation method to obtain its LP-relaxation. We address the derived pricing problem through a polynomial time algorithm based on solvers for the k-cardinality assignment problem. We insert this lower bound method in a two-phase branch and price algorithm in order to obtain the optimal solutions. To compare our new exact method with the one proposed in literature to solve the SS/TDMA optimization problem without cardinality constraint, we extend this older method to consider the cardinality constraint. The final computational experiments, comparing our new method with other already known methods, show the efficiency of our algorithms.     

Optimal multi-layered congestion based pricing schemes for enhanced QoS

Pricing is an effective tool to control congestion and achieve quality of service (QoS) provisioning for multiple differentiated levels of service. In this paper, we consider the problem of pricing for congestion control in the case of a network of nodes with multiple queues and multiple grades of service.We present a closed-loop multi-layered pricing scheme and propose an algorithm for finding the optimal state dependent price levels for individual queues, at each node. This is different from most adaptive pricing schemes in the literature that do not obtain a closed-loop state dependent pricing policy. The method that we propose finds optimal price levels that are functions of the queue lengths at individual queues. Further, we also propose a variant of the above scheme that assigns prices to incoming packets at each node according to a weighted average queue length at that node. This is done to reduce frequent price variations and is in the spirit of the random early detection (RED) mechanism used in TCP/IP networks.We observe in our numerical results a considerable improvement in performance using both of our schemes over that of a recently proposed related scheme in terms of both throughput and delay performance. In particular, our first scheme exhibits a throughput improvement in the range of 67–82% among all routes over the above scheme.     

Tabu marking scheme to speedup IP traceback

The IP traceback is an important mechanism in defending against distributed denial-of-service (DDoS) attacks. In this paper, we propose a probabilistic packet marking (PPM) scheme, Tabu Marking Scheme (TMS), to speedup IP traceback. The key idea of “tabu mark” is that, a router still marks packets probabilistically, but regards a packet marked by an upstream router as a tabu and does not mark it again. We study the impact of the traffic aggregation on the convergence behavior of PPM schemes. Furthermore we derive a new analytical result on the partial coupon collection problem, which is a powerful tool applicable for computing the mean convergence time of any PPM scheme. Our study shows that the idea of “tabu mark” not only helps a PPM scheme that allows overwriting to reduce the convergence time under a DDoS attack, but also ensures the authentication of the routers’ markings.     

Strategic Pricing in Next-Hop Routing with Elastic Demands

We consider a model of next-hop routing by self-interested agents. In this model, nodes in a graph (representing ISPs, Autonomous Systems, etc.) make pricing decisions of how much to charge for forwarding traffic from each of their upstream neighbors, and routing decisions of which downstream neighbors to forward traffic to (i.e., choosing the next hop). Traffic originates at a subset of these nodes that derive a utility when the traffic is routed to its destination node; the traffic demand is elastic and the utility derived from it can be different for different source nodes. Our next-hop routing and pricing model is in sharp contrast with the more common source routing and pricing models, in which the source of traffic determines the entire route from source to destination. For our model, we begin by showing sufficient conditions for prices to result in a Nash equilibrium, and in fact give an efficient algorithm to compute a Nash equilibrium which is as good as the centralized optimum, thus proving that the price of stability is 1. When only a single source node exists, then the price of anarchy is 1 as well, as long as some minor assumptions on player behavior is made. The above results hold for arbitrary convex pricing functions, but with the assumption that the utilities derived from getting traffic to its destination are linear. When utilities can be non-linear functions, we show that Nash equilibrium may not exist, even with simple discrete pricing models.     

ADER: Arbitrary High Order Godunov Approach

This paper concerns the construction of non-oscillatory schemes of very high order of accuracy in space and time, to solve non-linear hyperbolic conservation laws. The schemes result from extending the ADER approach, which is related to the ENO/WENO methodology. Our schemes are conservative, one-step, explicit and fully discrete, requiring only the computation of the inter-cell fluxes to advance the solution by a full time step; the schemes have optimal stability condition. To compute the intercell flux in one space dimension we solve a generalised Riemann problem by reducing it to the solution a sequence of m conventional Riemann problems for the kth spatial derivatives of the solution, with k=0, 1,..., m–1, where m is arbitrary and is the order of the accuracy of the resulting scheme. We provide numerical examples using schemes of up to fifth order of accuracy in both time and space.     

An efficient dynamic programming algorithm for a special case of the capacitated lot-sizing problem

In this paper we consider the capacitated lot-sizing problem (CLSP) with linear costs. It is known that this problem is NP-hard, but there exist special cases that can be solved in polynomial time. We derive a new O(T²) algorithm for the CLSP with non-increasing setup costs, general holding costs, non-increasing production costs and non-decreasing capacities over time, where T is the length of the model horizon. We show that in every iteration we do not consider more candidate solutions than the O(T²) algorithm proposed by [Chung and Lin, 1988. Management Science 34, 420–6]. We also develop a variant of our algorithm that is more efficient in the case of relatively large capacities. Numerical tests show the superior performance of our algorithms compared to the algorithm of [Chung and Lin, 1988. Management Science 34, 420–6].     

ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows

We develop a new family of well-balanced path-conservative quadrature-free one-step ADER finite volume and discontinuous Galerkin finite element schemes on unstructured meshes for the solution of hyperbolic partial differential equations with non-conservative products and stiff source terms. The fully discrete formulation is derived using the recently developed framework of explicit one-step P_NP_M schemes of arbitrary high order of accuracy in space and time for conservative hyperbolic systems [Dumbser M, Balsara D, Toro EF, Munz CD. A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes. J Comput Phys 2008;227:8209–53]. The two key ingredients of our high order approach are: first, the high order accurate P_NP_M reconstruction operator on unstructured meshes, using the WENO strategy presented in [Dumbser M, Käser M, Titarev VA Toro EF. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J Comput Phys 2007;226:204–43] to ensure monotonicity at discontinuities, and second, a local space–time Galerkin scheme to predict the evolution of the reconstructed polynomial data inside each element during one time step to obtain a high order accurate one-step time discretization. This approach is also able to deal with stiff source terms as shown in [Dumbser M, Enaux C, Toro EF. Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. J Comput Phys 2008;227:3971–4001]. These two key ingredients are combined with the recently developed path-conservative methods of Parés [Parés C. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J Numer Anal 2006;44:300–21] and Castro et al. [Castro MJ, Gallardo JM, Parés C. High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems. Math Comput 2006;75:1103–34] to treat the non-conservative products properly. We show applications of our method to the two-layer shallow water equations as well as applications to the recently published depth-averaged two-fluid flow model of Pitman and Le [Pitman EB, Le L. A two-fluid model for avalanche and debris flows. Philos Trans Roy Soc A 2005;363:1573–601].     

A Web marketing system with automatic pricing

We propose a new scheme of ‘automatic pricing' for digital contents, and describe an implemented system as well as concrete pricing algorithms for it. Automatic pricing refers to a methodology of automatically setting sales prices to optimal prices, based on past prices and sales. In particular, we consider the case in which automatic pricing is done in order to maximize the profit of an on-line marketing site. We describe a demo site for on-line marketing with automatic pricing, which we call ‘digiprice'. We will also describe the concrete pricing algorithms we employ in digiprice, and report on preliminary performance evaluation experiments we conducted using simulated data. The results of experimentation verify that our methods are practical in terms of both the speed of convergence to the optimal price and computational efficiency.     

Optimal Algorithms for <Emphasis Type="Italic">k</Emphasis>-Search with Application in Option Pricing

In the k-search problem, a player is searching for the k highest (respectively, lowest) prices in a sequence, which is revealed to her sequentially. At each quotation, the player has to decide immediately whether to accept the price or not. Using the competitive ratio as a performance measure, we give optimal deterministic and randomized algorithms for both the maximization and minimization problems, and discover that the problems behave substantially different in the worst-case. As an application of our results, we use these algorithms to price “lookback options”, a particular class of financial derivatives. We derive bounds for the price of these securities under a no-arbitrage assumption, and compare this to classical option pricing. J. Lorenz is partially supported by UBS AG. K. Panagiotou is partially supported by the SNF, grant number: 200021-107880/1.     

On using deterministic functions to reduce randomness in probabilistic algorithms

We show the existence of nonuniform schemes for the following sampling problem: Given a sample space with n points, an unknown set of size n/2, and s random points, it is possible to generate deterministically from them s + k points such that the probability of not hitting the unknown set is exponentially smaller in k than 2^−s. Tight bounds are given for the quality of such schemes. Explicit, uniform versions of these schemes could be used for efficiently reducing the error probability of randomized algorithms. A survey of known constructions (whose quality is very far from the existential result) is included.     

Competitive equilibrium in e-commerce: Pricing and outsourcing

The success of firms engaged in e-commerce depends on their ability to understand and exploit the dynamics of the market. One component of this is the ability to extract maximum profit and minimize costs in the face of the harsh competition that the internet provides. We present a general framework for modeling the competitive equilibrium across two firms, or across a firm and the market as a whole. Within this framework, we study pricing choices and analyze the decision to outsource IT capability. Our framework is novel in that it allows for any number of distributions on usage levels, price–QoS tradeoffs, and price and cost structures.     

Comparison of transform coding techniques for two-dimensional arbitrarily shaped images

Envisioned advanced multimedia video services include arbitrarily shaped (AS) image segments as well as regular rectangular images. Image segments of the TV weather report produced by the chromo-key technique [1] and image segments produced by video analysis and image segmentation [2–4] are typical examples of AS image segments. This paper explores efficient intraframe transform coding techniques for general two-dimensional (2D) AS image segments, treating the traditional rectangular images as a special case. In particular, we focus on the transform coding of the partially defined image blocks along the boundary of the AS image segments. We recognize two different approaches — thebrute force transform coding approach and theshape-adaptive transform coding approach. The former fills the uncovered area with the optimal redundant data such that the resulting transform spectrum is compact. A simple but efficient mirror image extension technique is proposed. Once augmented into full image blocks, these boundary blocks can be processed by traditional block-based transform techniques like the popular discrete cosine transform (DCT). In the second approach, we change either the transform basis or the coefficient calculation process adaptively based on the shape of the AS image segment. We propose an efficientshape-projected problem formulation to reduce the dimension of the problem. Existing coding algorithms, such as the orthogonal transform by Gilge [5] and the iterative coding by Kaup and Aach [6], can be interpreted intuitively. We also propose a new adaptive transform based on the same principle as that used in deriving the DCT from the optimal Karhunen-Loeve transform (KLT). We analyze the tradeoff relationship between compression performance, computational complexity, and codec complexity for different coding schemes. Simulation results show that complicated algorithms (e.g., iterative, adaptive) can improve the quality by 5–10 dB at some computational or hardware cost. Alternatively, the simple mirror image extension technique improves the quality by 3–4 dB without any overheads. The contributions of this paper lie in efficient problem formulations, new transform coding techniques, and numerical tradeoff analyses.