This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete; furthermore, financial assets are modeled by Itô processes....

In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE).

"It is a fairly complete introduction accessible to advanced undergraduates; Also covers more advanced aspects of interest rate modeling; Includes many graphs and code illustrating the modeling of interest rates; Each chapter is accompanied with exercises and their complete solutions."

We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating market option prices and local volatility using deep neural networks. Our method uses the initial-boundary value problem of the underlying Dupire's...

"Introduction to Stochastic Finance with Market Examples, Second Edition presents an introduction to pricing and hedging in discrete and continuous time financial models, emphasizing both analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models...