Laplace transformation is one of the most popular methods of solution of diffusion equations in many areas of science and technology. It is much less used in financial engineering. One reason is obvious: it is not supposed to be a way to solve a Nobel Prize winning problem. Another one is...

This paper discusses European option pricing under various discontinuous conditions: option and underlying prices as well as volatility and drift coefficients experience breaks. We consider vanilla and double-barrier options under double-exponential jump diffusion model with jump drift and jump...

Optimal execution of portfolio transactions is the essential part of algorithmic trading. The main result of this paper is the analytical equationfor the optimal trading trajectories with the assumption of exponential market recovery and short-time investment horizon. The formula has the same...

Medium frequency trading strategies include all trading activities, that do not require market microstructure analysis on one side and signi cantly depend on market impact on the other side. The most important di erence from high frequency trading is the ability to analyze big amount of data...

In this presentation we consider the management of big portfolios that risk trading desks of major financial institutions usually execute on daily basis. We take into account overnight risk for multiple days liquidation algorithm. We also discuss market impact models and the difference between...

The market impact (MI) of Volume Weighted Average Price (VWAP) orders is a convex function of a trading rate, but most empirical estimates of transaction cost are concave functions. How is this possible? We show that isochronic (constant trading time) MI is slightly convex, and isochoric...

The market impact (MI) of Volume Weighted Average Price (VWAP) orders is a convex function of a trading rate, but most empirical estimates of transaction cost are concave functions. How is this possible? We show that isochronic (constant trading time) MI is slightly convex, and isochoric...

Optimal execution of portfolio transactions is the essential part of algorithmic trading. In this paper we present in simple analytical form the optimal trajectory for risk-averse trader with the assumption of exponential market recovery and short-time investment horizon.