"Mathematically, most of the interesting optimization problems can be formulated to optimize some objective function, subject to some equality and/or inequality constraints. This book introduces some classical and basic results of optimization theory, including nonlinear programming with...

The book deals with topics such as the pricing of various contingent claims within different frameworks, risk-sensitive problems, optimal investment, defaultable term structure, etc. It also reflects on some recent developments in certain important aspects of mathematical finance. Contents:...

Self-financing optimal investment problem is considered in an incomplete market. The general existence of optimal portfolios is discussed via variational method of stochastic optimal control and the theory of (forward-) backward stochastic differential equations.