This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

Information is crucial to make good decisions, but obtaining and providing information often comes at a cost. Consumers and firms both need to balance these costs and benefits of obtaining and providing information in order to make the best decisions. The research in this thesis investigates several questions that pertain to the acquisition and provision of information. In the first part of this thesis it is assumed that consumers are not fully informed about the prices or availability of a product they want to buy. Consumers can search for information, but this comes at a cost. At the same time, shops can influence these costs. In the first two studies in this part, shops have the possibility to advertise. An advertisement provides information to consumers and reduces the search costs. We investigate, among other things, the pricing behavior of shops and the relation between search and advertising. The third study in this part of the thesis considers the location choice of shops. Locating together in a shopping mall reduces the search costs of consumers. This increases the competition between shops and lowers the prices, but we show that at the same time the sales volume increases. The total effect of locating together on profits is generally positive. The second part of this thesis considers director ties (also named interlocks). A director who has several directorships in different firms can serve as an information bridge between the different firms. At the same time, interlocking directors are busy and form a homogenous group. Data from the Netherlands show that in The Netherlands the positive information providing effect of interlocks is outweighed by a negative busyness and homogenous group effect.