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Register a new userTrading with Small Price Impact
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Added by
Johannes Muhle-Karbe
Publication date
2014
fields
Financial
and research's language is
English
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No Arabic abstract
An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. These results shed light on the general structure of the problem at hand, and also unveil close connections to optimal execution problems and to other market frictions such as proportional and fixed transaction costs.
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We study portfolio selection in a model with both temporary and transient price impact introduced by Garleanu and Pedersen (2016). In the large-liquidity limit where both frictions are small, we derive explicit formulas for the asymptotically optimal trading rate and the corresponding minimal leading-order performance loss. We find that the losses are governed by the volatility of the frictionless target strategy, like in models with only temporary price impact. In contrast, the corresponding optimal portfolio not only tracks the frictionless optimizer, but also exploits the displacement of the market price from its unaffected level.
Executing a basket of co-integrated assets is an important task facing investors. Here, we show how to do this accounting for the informational advantage gained from assets within and outside the basket, as well as for the permanent price impact of market orders (MOs) from all market participants, and the temporary impact that the agents MOs have on prices. The execution problem is posed as an optimal stochastic control problem and we demonstrate that, under some mild conditions, the value function admits a closed-form solution, and prove a verification theorem. Furthermore, we use data of five stocks traded in the Nasdaq exchange to estimate the model parameters and use simulations to illustrate the performance of the strategy. As an example, the agent liquidates a portfolio consisting of shares in Intel Corporation (INTC) and Market Vectors Semiconductor ETF (SMH). We show that including the information provided by three additional assets, FARO Technologies (FARO), NetApp (NTAP) and Oracle Corporation (ORCL), considerably improves the strategys performance; for the portfolio we execute, it outperforms the multi-asset version of Almgren-Chriss by approximately 4 to 4.5 basis points.
Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem using singular perturbation methods. We prove, by constructing sub- and super-solutions, that the approximations are accurate to the specified order. Finally, we perform some numerical experiments to illustrate the effect that stochastic trading frictions have on optimal trading.
This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive portfolio optimization on the finite time horizon. We study the problem by using a probabilistic approach to establish the existence and uniqueness of the classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We also implement a numerical scheme to investigate the behavior of solutions for different values of the initial portfolio wealth, the maturity, and the risk of aversion parameter.
A simple trading model based on pair pattern strategy space with holding periods is proposed. Power-law behaviors are observed for the return variance $sigma^2$, the price impact $H$ and the predictability $K$ for both models with linear and square root impact functions. The sum of the traders wealth displays a positive value for the model with square root price impact function, and a qualitative explanation is given based on the observation of the conditional excess demand $<A|u>$. An evolutionary trading model is further proposed, and the elimination mechanism effectively changes the behavior of the traders highly performed in the model without evolution. The trading model with other types of traders, e.g., traders with the MGs strategies and producers, are also carefully studied.
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