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In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamics of their aggregated inventory considering a proper scaling limit. The resulting price impact profile is shown to depend on the characteristics and relative importance of their inventories. The model is flexible enough to reproduce the empirically documented power law behavior of the price impact function. For any choice of the market makers characteristics, optimal execution within this modeling approach can be recast as a linear-quadratic stochastic control problem. The value function and the associated optimal trading rate can be obtained semi-explicitly subject to solving a differential matrix Riccati equation. Numerical simulations are conducted to illustrate the performance of the resulting optimal liquidation strategy in relation to standard benchmarks. Remarkably, they show that the increase in performance is determined by a substantial reduction of higher order moment risk. [ABSTRACT FROM AUTHOR]

In this paper we study optimal trading strategies in a financial market in which stock returns depend on a hidden Gaussian mean reverting drift process. Investors obtain information on that drift by observing stock returns. Moreover, expert opinions in the form of signals about the current state of the drift arriving at fixed and known dates are included in the analysis. Drift estimates are based on Kalman filter techniques. They are used to transform a power utility maximization problem under partial information into an optimization problem under full information where the state variable is the filter of the drift. The dynamic programming equation for this problem is studied and closed-form solutions for the value function and the optimal trading strategy of an investor are derived. They allow to quantify the monetary value of information delivered by the expert opinions. We illustrate our theoretical findings by results of extensive numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of optimal management of renewable resources such as agricultural commodities and fishery production. For that purpose, we consider the population associated with such commodities and assume that its size evolves according to a logistic growth model with a predation term given by a Holling type- n functional response. Additionally, we assume that such population is subject to random fluctuations, modeled by a diffusive term driven by a one-dimensional Brownian motion and having a power-type coefficient, thus endowing the model under consideration with the property of having constant elasticity of variance. Since the stochastic differential equation associated with this model does not fit the standard assumptions in the stochastic optimal control literature, namely sublinear growth, we develop an appropriate version of the dynamic programming principle for the problem under consideration herein, proceeding also to provide a characterization of the optimal harvesting strategies and discuss some qualitative properties of the corresponding value function. [ABSTRACT FROM AUTHOR]

For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step t, the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time steps t, t,..., T; at the next time step t, he is able to formulate a new optimization problem starting at time t that yields a new sequence of optimal decision rules. This process can be continued until the final time T is reached. A family of optimization problems formulated in this way is said to be dynamically consistent if the optimal strategies obtained when solving the original problem remain optimal for all subsequent problems. The notion of dynamic consistency, well-known in the field of economics, has been recently introduced in the context of risk measures, notably by Artzner et al. (Ann. Oper. Res. 152(1):5-22, ) and studied in the stochastic programming framework by Shapiro (Oper. Res. Lett. 37(3):143-147, ) and for Markov Decision Processes (MDP) by Ruszczynski (Math. Program. 125(2):235-261, ). We here link this notion with the concept of 'state variable' in MDP, and show that a significant class of dynamic optimization problems are dynamically consistent, provided that an adequate state variable is chosen. [ABSTRACT FROM AUTHOR]

The subject of this paper is modelling and optimal control of consumption and exploration of non-renewable resources via piecewise-deterministic Markov processes (PDP). In general, one assumes that new reserves are found at random times T1, T2, T3,…, where the inter-arrival times are exponentially distributed. The amount of resource found at each Ti is also a random variable with a given distribution. This process falls into the category of PDP. In this paper, we clearly show bow one can apply the PDP optimal control theory to the optimal consumption and exploration of non-renewable resources under uncertain exploration. The advantage of using a PDP model is that no matter how complicated the dynamics, utility function and distribution functions are, as long as they satisfy some mild assumptions, one can easily transform the problem into a deterministic optimal control problem, which can be solved iteratively with guaranteed convergence for the value function. [ABSTRACT FROM AUTHOR]