The paper investigates a problem of bounded risk portfolio selection for a multi-period market in the case when only historical prices are available, and all market parameters are not observable. We present a strategy which bounds risk closely to a risk-free investment and guarantees at the same...

We study an optimal investment problem for a diffusion market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are not necessarily adapted to the driving Brownian motion, and their distributions are unknown, but they are supposed to...

The paper suggest a modification of an American option such that the option holder can exercise the option early before the expiration, and he or she can retract later this decision to exercise. This feature gives additional flexibility and risk protection for the option holder. The contract...

We investigate the possibility of statistical evaluation of the market completeness for discrete timestock market models. It is known that the market completeness isnot a robust property: small random deviations of the coefficientsconvert a complete market model into a incomplete one. The...

The paper presents a pricing rule for market models with random volatility with an uncertainty in its evolution law. It is shown that the most popular existing models allow a possibility that the option price calculated for random volatility with an error in volatility forecasts is lower that...

We study optimal investment problem for a market model where the evolution of risky assets is described by Ito's equations. The risk-free rate, the appreciation rates, and the volatility of the stocks are all random; they are not necessary adapted to the driving Brownian motion, their...

We consider a problem of optimal gradual liquidation of equity from a risky asset for continuous time stochastic market model. The owner of the risky asset uses this equity as a source of steady cash flow by borrowing money permanently against thisequity. At the terminal time, there is no equity...

The paper studies multi-period discrete time market models with serial correlations. We found the optimal strategy in mean-variance and goal achieving setting for the case when there are serial correlations and when the parameter process that causes correlations is currently observable

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