634 research outputs found

    Asset Pricing with Delayed Consumption Decisions

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    The attempt to match characteristics of asset pricing models such as the risk-free interest rate, equity premium and the Sharpe ratio for models with instantaneous consumption decisions in the context of stochastic growth models has not been very successful. Many recent versions of asset pricing models have, in order to match those financial characteristics better with the data, employed habit formation models where there is a delay in consumption decisions. Yet the results of those studies may depend on the solution techniques employed to solve the stochastic dynamic optimization model. In this paper a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the above mentioned asset price characteristics with delayed consumption decisions, where the delayed consumption decision is treated as an additional state variable of the model. Since our method produces only negligible errors it is suitable to be used as solution technique for elaborate stochastic growth models with a delayed decision structure.stochastic growth, habit formation, stochastic DP, adaptive grid, asset pricing

    A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation

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    In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the size of the local hypercubes involved in the regressions, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants. This model takes into account electricity demand, cointegrated fuel prices, carbon price and random outages of power plants. It computes the optimal level of investment in each generation technology, considered as a whole, w.r.t. the electricity spot price. This electricity price is itself built according to a new extended structural model. In particular, it is a function of several factors, among which the installed capacities. The evolution of the optimal generation mix is illustrated on a realistic numerical problem in dimension eight, i.e. with two different technologies and six random factors

    An LMI Framework for Contraction-based Nonlinear Control Design by Derivatives of Gaussian Process Regression

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    Contraction theory formulates the analysis of nonlinear systems in terms of Jacobian matrices. Although this provides the potential to develop a linear matrix inequality (LMI) framework for nonlinear control design, conditions are imposed not on controllers but on their partial derivatives, which makes control design challenging. In this paper, we illustrate this so-called integrability problem can be solved by a non-standard use of Gaussian process regression (GPR) for parameterizing controllers and then establish an LMI framework of contraction-based control design for nonlinear discrete-time systems, as an easy-to-implement tool. Later on, we consider the case where the drift vector fields are unknown and employ GPR for functional fitting as its standard use. GPR describes learning errors in terms of probability, and thus we further discuss how to incorporate stochastic learning errors into the proposed LMI framework

    Asset pricing with dynamic programming

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    Abstract: The study of asset price characteristics of stochastic growth models such as the risk-free interest rate, equity premium and the Sharpe-ratio has been limited by the lack of global and accurate methods to solve dynamic optimization models. In this paper a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the asset price characteristics of a stochastic growth model. The stochastic growth model is of the type as developed by Brock and Mirman (1972) and Brock (1979, 1982). It has become the baseline model in the stochastic dynamic general equilibrium literature. In a ¯rst step, in order to test our pro-cedure, it is applied to this basic stochastic growth model for which the optimal consumption and asset prices can analytically be computed. Since, as shown, our method produces only negligible errors, as compared to the analytical solution, in a second step, we apply it to more elaborate stochastic growth models with adjustment costs and habit formation. In the latter model prefer-ences are not time separable and past consumption acts as a constraint on current consumption. This model gives rise to an additional state variable. We here too apply our stochastic version of
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