Connections between a system of Forward-Backward SDEs and Backward Stochastic PDEs related to the utility maximization problem

Connections between a system of Forward-Backward SDEs and Backward Stochastic PDEs related to the utility maximiza- tion problem is established. Besides, we derive another version of FBSDE of the same problem and prove an existence of a solutio

Forbidden zones for the expectation. New mathematical results for behavioral and social sciences

A forbidden zones theorem, mathematical approach and model are proposed in the present article. In particular, the approach supposes that people decide as if there were some biases of the expectations of measurement data. The article is motivated by the need of a theoretical support for the practical analysis performed for the purposes of utility and prospect theories, behavioral economics, psychology, decision and social sciences. Possible general consequences and applications of the theorem and approach for a noise and biases of measurement data are preliminary considered as well

Forward backward semimartingale systems for utility maximization

We consider the problem of maximizing the expected utility of terminal wealth with a terminal random liability when the underlying asset price process is a continuous semimartingale. The optimal strategy is characterized in terms of a semimartingale forward backward system of equations. The results cover the cases of exponential, logarithmic and power utilities, which we analyze as illustrative example

Forward backward semimartingale systems for utility maximization

We consider the problem of maximizing the expected utility of terminal wealth with a terminal random liability when the underlying asset price process is a continuous semimartingale. The optimal strategy is characterized in terms of a semimartingale forward backward system of equations. The results cover the cases of exponential, logarithmic and power utilities, which we analyze as illustrative examples