We consider the portfolio optimization problem for the criterion of maximization of expected terminal log-utility. The underlying market model is a regime-switching diffusion model where the regime is determined by an unobservable factor process forming a finite state Markov process. The main...

We study the applicability of the method of Dynamic Programming (DP) for the solution of a general class of sequential decision problems under uncertainty, that may more commonly be referred to as discrete-time control problems under uncertainty. The uncertainty is due to the fact that the...

The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are...

We consider the problem of maximization of expected utility from terminal wealth in a market model that is driven by a possibly not fully observable factor process and that takes explicitly into account the possibility of default for the individual assets as well as contagion (direct and...

This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.