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....

The paper studies estimation of implied volatility and the impact of the choice of the corresponding risk-free rate proxy. We suggest to analyze the implied volatility and the risk-free rate proxy inferred in conjunction from the observed option prices. We formulate and solve an overdefined...

This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary...

Dynamic Portfolio Strategies: Quantitative Methods and Empirical Rules for Incomplete Information investigates optimal investment problems for stochastic financial market models. It is addressed to academics and students who are interested in the mathematics of finance, stochastic processes, and...

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...

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...

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,...