We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving Brownian motion, and they are supposed to be currently...

The paper studies estimation of parameters of diffusion market models from historical option prices. A method of reducing the impact of the stock price movements on the dynamically implied parameters is suggested. It is shown that a certain selection of the options can deliver a smooth in time...

By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable processes generated by a...

We discuss the problems of strategy selection in the framework of mathematical finance, stochastic control, and risk management in finance and economics. A problem setting that takes in to account a possibility of short term forecasting for market parameters is suggested. In this setting,...

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...

For the problem of continuous time optimal portfolio selection, we found that the optimal strategies for investors with different performance criterions can be constructed using a limited number of fixed processes (mutual funds), for a incomplete market with a larger number of available risky...

We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the...

We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two independent Gaussian processes one of which is smooth in the sense that it is differentiable in mean square. We...

We suggest a modification of an American option such that the option holder can exercise the option early before the expiration and can revert later this decision to exercise; it can be repeated a number of times. This feature gives additional flexibility and risk protection for the option...