Pricing in an equilibrium based model for a large investor

We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the market maker quotes the prices such that by taking the other side of the investor’s demand, the market maker will arrive at maturity with the maximal expected utility of the terminal wealth. Within this model we provide an explicit recursive pricing formula for an exponential utility function, as well as an asymptotic expansion for the price for a “small” simple demand.     

Separating Cycles in Doubly Toroidal Embeddings

 We show that every 4-representative graph embedding in the double torus contains a noncontractible cycle that separates the surface into two pieces. As a special case, every triangulation of the double torus in which every noncontractible cycle has length at least 4 has a noncontractible cycle that separates the surface into two pieces. Received: May 22, 2001 Final version received: August 22, 2002 RID="*" ID="*" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070613 RID="†" ID="†" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070430     

Convergence analysis and error estimates for a parallel algorithm for solving the Navier-Stokes equations

Summary. This paper is concerned with the analysis of the convergence and the derivation of error estimates for a parallel algorithm which is used to solve the incompressible Navier-Stokes equations. As usual, the main idea is to split the main differential operator; this allows to consider independently the two main difficulties, namely nonlinearity and incompressibility. The results justify the observed accuracy of related numerical results. Received April 20, 2001 / Revised version received May 21, 2001 / Published online March 8, 2002 RID="*" ID="*" Partially supported by D.G.E.S. (Spain), Proyecto PB98–1134 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="*" ID="*" Partially supported by D.G.E.S. (Spain), Proyecto PB98–1134 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="**" ID="**" Partially supported by D.G.E.S. (Spain) Proyecto PB96–0986     

An algorithm for ordinal sorting based on ELECTRE with categories defined by examples

This work proposes a Progressive Assisted Sorting Algorithm (PASA) based on a multicriteria evaluation ELECTRE-type method. The purpose of the PASA is to aid a decision maker to progressively sort a set of alternatives into a set of categories, which we considered are ordered (ordinal sorting), following a consistency principle. We consider the principle that if an alternative outranks (is as good as) a second one, then it must belong to the same category or to a better category. The set of alternatives already sorted by the decision maker will implicitly define the categories, and will constrain the range of categories where other alternatives may be sorted. We show how the same idea may be used in an aggregation/disaggregation approach, considering some parameters of ELECTRE are not fixed a priori, but are constrained only by the examples provided. In this context, we establish a “convex-shape property” stating that the range of possible categories for an alternative is always an interval of categories. A discussion contrasting this approach with ELECTRE TRI is included in the conclusions.     

Locally Well-Dominated and Locally Independent Well-Dominated Graphs

 In this article we present characterizations of locally well-dominated graphs and locally independent well-dominated graphs, and a sufficient condition for a graph to be k-locally independent well-dominated. Using these results we show that the irredundance number, the domination number and the independent domination number can be computed in polynomial time within several classes of graphs, e.g., the class of locally well-dominated graphs. Received: September 13, 2001 Final version received: May 17, 2002 RID="*" ID="*" Supported by the INTAS and the Belarus Government (Project INTAS-BELARUS 97-0093) RID="†" ID="†" Supported by RUTCOR RID="*" ID="*" Supported by the INTAS and the Belarus Government (Project INTAS-BELARUS 97-0093) 05C75, 05C69 Acknowledgments. The authors thank the referees for valuable suggestions.     

Computational complexity of stable partitions with B-preferences

Consider a special stable partition problem in which the player's preferences over sets to which she could belong are identical with her preferences over the most attractive member of a set and in case of indifference the set of smaller cardinality is preferred. If the preferences of all players over other (individual) players are strict, a strongly stable and a stable partition always exists. However, if ties are present, we show that both the existence problems are NP-complete. These results are very similar to what is known for the stable roommates problem. Received: July 2000/Revised: October 2002 RID="*" ID="*"  This work was supported by the Slovak Agency for Science, contract #1/7465/20 “Combinatorial Structures and Complexity of Algorithms”.     

Power indices and the veil of ignorance

We provide an axiomatic foundation of the expected utility preferences over lotteries on roles in simple superadditive games represented by the two main power indices, the Shapley-Shubik index and the Banzhaf index, when they are interpreted as von Neumann-Morgenstern utility functions. Our axioms admit meaningful interpretations in the setting proposed by Roth in terms of different attitudes toward risk involving roles in collective decision procedures under the veil of ignorance. In particular, an illuminating interpretation of `efficiency', up to now missing in this set up, as well as of the corresponding axiom for the Banzhaf index, is provided. November 7, 2002 RID="*" ID="*"  We want to thank M. Maschler, J. M. Zarzuelo and two referees for their comments. This research has been supported by the IVIE, and by the DGES of the Spanish Ministerio de Educación y Cultura, under project PB96-0247. The first author also acknowledges the financial support from the Ramón y Cajal Program initiated by the Spanish MCyT.     

Simple and immune relations on countable structures

 Let 𝒜 be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of 𝒜 in which the image of R (?R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on 𝒜 and R, a necessary and sufficient condition for the existence of a computable copy ℬ of 𝒜 in which the image of R (?R, resp.) is simple (immune, resp.). Received: 4 February 2001 Published online: 5 November 2002 RID="*" ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899. RID="*" ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899. RID="*" ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899.     

On the structure of rotation-invariant semigroups

 We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows from their other axioms. Received: 7 January 2002 / Revised version: 4 April 2002 / Published online: 19 December 2002 RID="*" ID="*" Supported by the National Scientific Research Fund Hungary (OTKA F/032782). Mathematics Subject Classification (2000): 20M14, 06F05 Key words or phrases: Residuated lattice – Conjunction for non-classical logics     

On the Classification of Self-Dual Codes over 𝔽5

 In this paper, we give the classification of self-dual 𝔽₅-codes of lengths 14 and 16. Up to equivalence, there are 53 and 535 such codes, respectively. It is also shown that there is no self-dual [18, 9, 8] code over 𝔽₅. Received: June 18, 2001 Final version received: April 9, 2002 RID="*" ID="*" Supported in part by the Academy of Finland under grants 44517 and 100500     

P2q hierarchical decomposition algorithm for quantile optimization: application to irrigation strategies design

Decision theory dealing with uncertainty is usually considering criteria such as expected, minimum or maximum values. In economic areas, the quantile criterion is commonly used and provides significant advantages. This paper gives interest to the quantile optimization in decision making for designing irrigation strategies. We developed P2q, a hierarchical decomposition algorithm which belongs to the branching methods family. It consists in repeating the creation, evaluation and selection of smaller promising regions. Opposite to common approaches, the main criterion of interest is the α-quantile where α is related to the decision maker risk acceptance. Results of an eight parameters optimization problem are presented. Quantile optimization provided optimal irrigation strategies that differed from thus reached with expected value optimization, responding more accurately to the decision maker preferences.