634 research outputs found
Asset Pricing with Delayed Consumption Decisions
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
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
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
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Game-Theoretic Safety Assurance for Human-Centered Robotic Systems
In order for autonomous systems like robots, drones, and self-driving cars to be reliably introduced into our society, they must have the ability to actively account for safety during their operation. While safety analysis has traditionally been conducted offline for controlled environments like cages on factory floors, the much higher complexity of open, human-populated spaces like our homes, cities, and roads makes it unviable to rely on common design-time assumptions, since these may be violated once the system is deployed. Instead, the next generation of robotic technologies will need to reason about safety online, constructing high-confidence assurances informed by ongoing observations of the environment and other agents, in spite of models of them being necessarily fallible.This dissertation aims to lay down the necessary foundations to enable autonomous systems to ensure their own safety in complex, changing, and uncertain environments, by explicitly reasoning about the gap between their models and the real world. It first introduces a suite of novel robust optimal control formulations and algorithmic tools that permit tractable safety analysis in time-varying, multi-agent systems, as well as safe real-time robotic navigation in partially unknown environments; these approaches are demonstrated on large-scale unmanned air traffic simulation and physical quadrotor platforms. After this, it draws on Bayesian machine learning methods to translate model-based guarantees into high-confidence assurances, monitoring the reliability of predictive models in light of changing evidence about the physical system and surrounding agents. This principle is first applied to a general safety framework allowing the use of learning-based control (e.g. reinforcement learning) for safety-critical robotic systems such as drones, and then combined with insights from cognitive science and dynamic game theory to enable safe human-centered navigation and interaction; these techniques are showcased on physical quadrotors—flying in unmodeled wind and among human pedestrians—and simulated highway driving. The dissertation ends with a discussion of challenges and opportunities ahead, including the bridging of safety analysis and reinforcement learning and the need to ``close the loop'' around learning and adaptation in order to deploy increasingly advanced autonomous systems with confidence
Asset pricing with dynamic programming
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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