The paper studies multi-stock discrete time market models with serial correlations and with some management costs. We found a market structure that ensures that the optimal strategy is myopic for the case of either power or log utility function.

This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the num\'eraire...

The optimal investment problem is studied for a continuous time incomplete market model. It is assumed that the risk-free rate, the appreciation rates, and the volatility of the stocks are all random; they are independent from the driving Brownian motion, and they are currently observable. It is...

The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the risk-free interest rate. In reality, the risk free interest...

The paper presents sufficient conditions of predictability for continuous time processes in deterministic setting. We found that processes with exponential decay on energy for higher frequencies are predictable in some weak sense on some finite time horizon defined by the rate of decay....