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## Robustness of equilibrium in the Kyle model of informed speculation

We analyze a static Kyle (Continuous auctions and insider trading. Princeton University, Princeton, 1983) model in which a risk-neutral informed trader can use arbitrary (linear or non-linear) deterministic strategies, and a finite number of market makers can use arbitrary pricing rules. We establish a strong sense in which the linear Kyle equilibrium is robust: the first variation in any agent’s expected payoff with respect to a small variation in his conjecture about the strategies of others vanishes at equilibrium. Thus, small errors in a market maker’s beliefs about the informed speculator’s trading strategy do not reduce his expected payoffs. Therefore, the original equilibrium strategies remain optimal and still constitute an equilibrium (neglecting the higher-order terms). We also establish that if a non-linear equilibrium exists, then it is not robust. © 2015 Springer-Verlag Berlin Heidelberg

We apply the suboptimal sequential nonparametric hypotheses testing approach for effectiveness of a statistical decision by sample space reducing. Numerical examples of the sample space reducing are given when an appropriate reducing makes it possible to construct robust sequential nonparametric hypotheses testing with a smaller mean duration time then one on the total sample space. © 2014 IEEE.

The general issues of determining the liquidation value are discussed, such as the choice of market liquidity risk model and the choice of a price benchmark for estimating transaction costs. The layout for the portfolio management process is proposed which is grounded on a previously developed approach to determining the liquidation value of a portfolio. It allows not only defining and linking the rational liquidation strategies for different time horizons but also considering some microstructural effects, such as volatility momentum, corresponding to the intervals between trading sessions.

Proceedings of the III International Conference in memory of V.I. Zubov "Stability and Control Processes (SCP 2015)".

Research of nonlinear dynamics of finance series has been widely discussed in literature since the 1980s with chaos theory as the theoretical background. Chaos methods have been applied to the S&P 500 stock index, stock returns from the UK and American markets, and portfolio returns. This work reviews modern methods as indicators of nonlinear stochastic behavior and also shows some empirical results for MICEX stock market high-frequency microstructure variables such as stock price and return, price change, spread and relative spread. It also implements recently developed recurrence quantification analysis approaches to visualize patterns and dependency in microstructure data.

Relaxation time is one of the most significant aspects of market liquidity. We study estimates of relaxation time of the limit order market after a shock triggered by sudden movement of price, large trade or news. We also provide formal definition of a shock on order-driven market.

We present robustness of the firm as an uninterrupted exchange of resources between the firm and owners of resources - stakeholders. We derive the model on the mutually accepted conditions of exchanges for the major resources and indicate the firm's limits to manipulate the exchange conditions. We also argue that temporary benevolent behavior of the firms towards one or several its stakeholders leads to accumulation of stakeholders' quasi-rent and contributes to the overall robustness of the firm.