This book is intended as a contribution to the theory of contingent claim valuation based on arbitrage considerations. It is concerned with preference-free valuations of contingent claims (such as options written on a stock) in frictionless multiperiod securities markets that do not permit arbitrage profits. Besides the question of pricing it considers the possibility of hedging in securities markets. The research reported in this book was carried out at the Institut fUr Gesellschafts- und Wirtschaftswissenschaften, University of Bonn. While working in this field and preparing this monograph I received helpful comments and encouragement from many people, and I would like to thank all of them. Special thanks are due to Prof. Dr. Dieter Sonder- mann. He first stimulated my interest in the theory of contingent claim valuation and commented on my work at various stages. Furthermore, I would like to thank Profs. Martin Hellwig, Peter Schonfeld and Klaus SchUrger, all University of Bonn, for helpful comments on earlier ver- sions of this monograph. Parts of this monograph were presented at va- rious meetings including the European Meeting of the Econometric Socie- ty, Pisa 1983, the European Meeting of the Econometric Society, Madrid 1984, and the third Conference "Geld, Banken und Versicherungen", Karls- ruhe 1984. I greatly appreciate comments of Profs. Stephen Ross, Yale University, and Michael Brennan, UCLA. I take this opportunity to ex- press my indebtness to my colleague Dr. Shinichiro Nakamura for his con- stant encouragement during the laborious process of writing this mono- graph.