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Using the Malliavin calculus in time inhomogeneous jump-diffusion models, we obtain an expression for the sensitivity Theta of an option price (with respect to maturity) as the expectation of the option payoff multiplied by a stochastic weight. This expression is used to design efficient numerical algorithms that are compared with traditional finite-difference methods for the computation of Theta. Our proof can be viewed as a generalization of Dupire's integration by parts to arbitrary and possibly non-smooth payoff functions. In the time homogeneous case, Theta admits an expression from the Black-Scholes PDE in terms of Delta and Gamma but the representation formula obtained in this way is different from ours. Numerical simulations are presented in order to compare the efficiency of the finite-difference and Malliavin methods.Applied mathematical finance, European financial markets, Computational finance, Financial mathematics,

Social capital theory generally analyses network structures by focusing on the connections between players. However, it has been suggested by several authors that the absence of relations in a network or ‘structural holes’ is meaningful. The aim of our paper is to provide a global survey and appraisal of the academic research on structural holes and discuss its main measurements. We adopt a bibliometric approach and identify a typology of practices, developments, and issues related to structural holes. We highlight a strand of work on operationalization of structural holes, and discuss the various measures they propose. We provide numerical examples emphasizing the respective advantages and limitations of the studied measures. Based on our results, we propose a guide to using existing measures of structural holes according to the type (simple or complex) of network.

Abstract. We examine a stochastic optimal control problem in a financial market driven by a Lévy process with filtration F = (Ft) t∈ [0,T ] . We assume that in the market there are two kinds of investors with different levels of information: an uninformed agent whose information coincides with the natural filtration of the price processes and an insider who has more information than the uninformed agent. When optimal consumption and investment exist, we identify some necessary conditions and find the optimal strategy by using forward integral techniques. We conclude by giving some examples.

Social capital is decisive to many of strategic objectives of organizations. Although it has been extensively defined in the literature, social capital continues to be discussed in particular concerning its measurement. What is the usability of the existing indicators of social capital? How do managers decide which one they would prefer? An overview of the literature reveals that there are very few measurements of social capital and those which have already developed are very complex. Direct measurements appear to provide a better understanding of the complexity of relationships than aggregated measurements. Yet, we show that they are of unsatisfactory quality. Using simple counter-examples, we advance that they give rise to contradictions. From this discussion and using Graph Theory, we propose two complementary indicators of social capital which we call “relational strength” and “relational potential”. These operational indicators can be handled by any actors to position themselves within their social sphere.

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To cite this version:Emmanuelle Augeraud-Véron, Delphine David. A stochastic overlapping generation model with a continuum of agents. Lukasz Stettner. Advances in Mathematics of Finance, Apr 2007, Bedlewo, Poland. 83, pp.27-36, 2008 A stochastic overlapping generation model with a continuum of agentsAbstract We consider a stochastic overlapping generations model for a continuum of individuals with finite lives in presence of a financial market. In this paper, agent's heterogeneity is given by the dates of birth of the households, on the contrary to standard models, in which each agent has his own aversion coefficient on his utility function. By means of the martingale arguments, we compute the agent's optimal consumption and portfolio. A characterization of interest rate trajectories is given by mixed-type functional differential equations and the stability of these trajectories is studied.

International audienceTools and Techniques for Economic Decision Analysis provides a thorough overview of decision models and methodologies in the context of business economics. Highlighting a variety of relevant issues on finance, economic policy, and firms and networks, this book is a reference source for managers, professionals, students, and academics interested in emerging developments for decision analysis