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

The paper studies discrete time mean-reverting market models. It is shown that a correct choice of initial conditions ensures existence of an equivalent martingale measure for any finite time horizon. This leads to a pricing rule for options and absence of arbitrage. Further, it is shown that...

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 study arbitrage opportunities and possible speculative opportunities for diffusion mean-reverting market models. We prove that the Novikov condition is satisfied for any time interval and for any set of parameters. It is non-trivial because the appreciation rate has conditionally Gaussian...

We consider optimal investment problems for a diffusion market model with non-observable random drifts that evolve as an Ito's process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a non-linear problem with a general...

We study a bond pricing problem for a case when the short term interest rate is a random process with unknown prior distribution and evolution law. We assume that there is a stock and options on this stock with observable prices; the stock volatility can be random. We assume that the option...

The paper studies option price models for diffusion market with random volatility and with pricing rules based on risk-neutral valuation. It is found that there are some properties of implied volatility that are presented for all possible risk neutral measures for the case when random historical...

The standard implied volatility definition presents its value as an implicit function of several parameters, including the risk-free interest rate. This approach ignores the fact that, in reality, the risk free interest rate is unknown and need to be forecasted, because the option price depends...