Оптимальные Алгоритмы Исполнения для Стратегических Трейдеров
We analyze optimal execution strategies when multiple traders are simultaneously involved in optimal execution. In this case, we obtain new trading strategies that follow from a direct extension of the mean variance approach of Grinold and Kahn, and Almgren and Chriss. However, as we show below, the proposed strategies can be quite different from the standard ones obtained in Grinold and Kahn, and Almgren and Chriss. This is because each trader (assumed to be rational) is trying to minimize her trading cost or "implementation shortfall" and therefore takes into account the price impacts caused by herself and all other traders. We also obtain a close form characterization for the dynamic Nash equilibrium in terms of the system of second-order ODEs, which can be solved explicitly. The resulting equilibrium strategies describe different types of predatory and defensive behavior, though aggregate order flow profile have some properties of standard Almgren, Chriss strategies, e.g. is monotoneous and convex. We show that the traders with smaller holdings are involved in predatory strategies, while traders with larger holdings tend to defend themselves against potential predators by following the delayed trading strategies. We also show that depending on liquidity and volatility parameters, predatory traders may be frontrunners or contrarian traders.
This article presents an engineering approach to estimating market resiliency based on analysis of the dynamics of a liquidity index. The method provides formal criteria for defining a “liquidity shock” on the market and can be used to obtain resiliency-related statistics for further research and estimation of this liquidity aspect. The developed algorithm uses the results of a spline approximation for observational data and allows a theoretical interpretation of the results. The method was applied to real data resulting in estimation of market resiliency for the given period.
The aim of this paper is to consider some problems with evaluation of the impact of high frequency trading on market liquidity. The first part is devoted to difficulties of disentangling the impact of high frequency on market liquidity from other relevant factors. The remainder of the paper is intended to discuss some issues affecting the evaluation of the influence of high frequency trading on particular aspects of market liquidity.
We use the imputation distribution procedure approach to ensure sustainable cooperation in a multistage game with vector payoffs. In order to choose a particular Pareto optimal and time consistent strategy profile and the corresponding cooperative trajectory we suggest a refined leximin algorithm. Using this algorithm we design a characteristic function for a multistage multicriteria game. Furthermore, we provide sufficient conditions for strong time consistency of the core.
The problem of optimal portfolio liquidation under transaction costs has been widely researched recently, thus producing several approaches to problem formulation and solving. Obtained results can be used for decision making during portfolio selection or automatic trading at high-frequency electronic markets. This work gives a review of modern studies in this field, comparing models and tracking their evolution. The paper also presents results of applying the most recent findings in this field to real MICEX shares high-frequency data and gives an interpretation of the results.
To ensure sustainable cooperation in multistage games with vector payoffs we use the payment schedule based approach. The main dynamic properties of cooperative solutions used in single-criterion multistage games are extended to multicriteria games.
We design two recurrent payment schedules that satisfy such advantageous properties as the efficiency and the time consistency conditions, non-negativity and irrational behavior proofness.
The paper examines the structure, governance, and balance sheets of state-controlled banks in Russia, which accounted for over 55 percent of the total assets in the country's banking system in early 2012. The author offers a credible estimate of the size of the country's state banking sector by including banks that are indirectly owned by public organizations. Contrary to some predictions based on the theoretical literature on economic transition, he explains the relatively high profitability and efficiency of Russian state-controlled banks by pointing to their competitive position in such functions as acquisition and disposal of assets on behalf of the government. Also suggested in the paper is a different way of looking at market concentration in Russia (by consolidating the market shares of core state-controlled banks), which produces a picture of a more concentrated market than officially reported. Lastly, one of the author's interesting conclusions is that China provides a better benchmark than the formerly centrally planned economies of Central and Eastern Europe by which to assess the viability of state ownership of banks in Russia and to evaluate the country's banking sector.
The paper examines the principles for the supervision of financial conglomerates proposed by BCBS in the consultative document published in December 2011. Moreover, the article proposes a number of suggestions worked out by the authors within the HSE research team.
The paper studies a problem of optimal insurer’s choice of a risk-sharing policy in a dynamic risk model, so-called Cramer-Lundberg process, over infinite time interval. Additional constraints are imposed on residual risks of insureds: on mean value or with probability one. An optimal control problem of minimizing a functional of the form of variation coefficient is solved. We show that: in the first case the optimum is achieved at stop loss insurance policies, in the second case the optimal insurance is a combination of stop loss and deductible policies. It is proved that the obtained results can be easily applied to problems with other optimization criteria: maximization of long-run utility and minimization of probability of a deviation from mean trajectory.