Methods of Mathematical Finance

This book is the sequel to Brownian Motion and Stochastic Calculus by the sameauthors. Within the context of Brownianmotiondriven asset prices it developscontin... » 

This book is the sequel to Brownian Motion and Stochastic Calculus by the sameauthors. Within the context of Brownianmotiondriven asset prices it developscontingent claim pricing and optimal consumptioninvestment in both completeand incomplete markets. The latter topic is extended to a study of equilibriumproviding conditions for existence and uniqueness of market prices whichsupport trading by several heterogeneous agents. Although much of theincompletemarket material is available in research papers these topics aretreated for the first time in a unified manner. The book contains an extensiveset of references and notes describing the field including topics not treatedin the book. This book will be of interest to researchers wishing to seeadvanced mathematics applied to finance. The material on optimal consumptionand investment leading to equilibrium is addressed to the theoretical financecommunity. The chapters on contingent claim valuation presents techniques ofpractical importance especially for pricing exotic options. TOCA BrownianMotion of Financial Markets. Contingent Claim Valuation in a Complete Market.SingleAgent Consumption and Investment. Equilibrium in a Complete Market.Contingent Claims in Incomplete Markets. Constrained Consumption andInvestment. «