Optimal Dimension of Transition Probability Matrices for Markov Chain Bootstrapping

� While the large portion of the literature on Markov chain (possibly of order higher than one) bootstrap methods has focused on the correct estimation of the transition probabilities, little or no attention has been devoted to the problem of estimating the dimension of the transition probability matrix. Indeed, it is usual to assume that the Markov chain has a one-step memory property and that the state space could not to be clustered, and coincides with the distinct observed values. In this paper we question the opportunity of such a standard approach. In particular we advance a method to jointly estimate the order of the Markov chain and identify a suitable clustering of the states. Indeed in several real life applications the "memory" of many processes extends well over the last observation; in those cases a correct representation of past trajectories requires a significantly richer set than the state space. On the contrary it can sometimes happen that some distinct values do not correspond to really "different states of a process; this is a common conclusion whenever, for example, a process assuming two distinct values in t is not affected in its distribution in t+1. Such a situation would suggest to reduce the dimension of the transition probability matrix. Our methods are based on solving two optimization problems. More specifically we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping: preserving the similarity between the observed and the bootstrap series and reducing the probabilities of getting a perfect replication of the original sample. A brief axiomatic discussion is developed to define the desirable properties for such optimal criteria. Two numerical examples are presented to illustrate the method. �order of Markov chains,similarity of time series,transition probability matrices,multiplicity of time series,partition of states of Markov chains,Markov chains,bootstrap methods

Market Dynamics When Agents Anticipate Correlation Breakdown

The aim of this paper is to analyse the effect introduced in the dynamics of a financial market when agents anticipate the occurrence of a correlation breakdown. What emerges is that correlation breakdowns can act both as a consequence and as a triggering factor in the emergence of financial crises rational bubbles. We propose a market with two kinds of agents: speculators and rational investors. Rational agents use excess demand information to estimate the variance-covariance structure of assets returns, and their investment decisions are represented as a Markowitz optimal portfolio allocation. Speculators are uninformed agents and form their expectations by imitative behavior, depending on market excess demand. Several market equilibria result, depending on the prevalence of one of the two types of agents. Differing from previous results in the literature on the interaction between market dynamics and speculative behavior, rational agents can generate financial crises, even without the speculator contribution

Optimal sales-mix and generation plan in a two-stage electricity market

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Transforming Sovereign Debts into Perpetuities through a European Debt Agency

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risk aversion in modeling of cap and trade mechanism and optimal design of emission markets

According to theoretical arguments, a properly designed emission trading system should help reaching pollution reduction at low social burden. Based on the theoretical work of environmental economists, cap-and-trade systems are put into operations all over the world. However, the practice from emissions trading yields a real stress test for the underlying theory and reveals a number of its weak points. This paper aims to fill the gap between general welfare concepts underlying understanding of liberalized market and specific issues of real-world emission market operation. In our work, we present a novel technique to analyze emission market equilibrium in order to address diverse questions in the setting of risk-averse market players. Our contribution significantly upgrades all existing models in this field, which neglect risk-aversion aspects at the cost of having a wide range of singularities in their conclusions, now resolved in our approach. Furthermore, we show how the architecture of an environmental market can be optimized under the realistic assumption of risk-aversion and which approximations must be met therefore

Relevant States and Memory in Markov Chain Bootstrapping and Simulation

Markov chain theory is proving to be a powerful approach to bootstrap highly nonlinear time series. In this work we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular the choice of memory lags and the aggregation of irrelevant states are obtained by looking for regularities in the transition probabilities. Our approach is based on an optimization model. More specifically we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping: preserving the “structural” similarity between the original and the simulated series and assuring a controlled diversification of the latter. A discussion based on information theory is developed to define the desirable properties for such optimal criteria. Two numerical tests are developed to verify the effectiveness of the method proposed here

Renewables, allowances markets, and capacity expansion in energy-only markets

We investigate the combined effect of an Emissions Trading System (ETS) and renewable energy sources on investments in electricity capacity in energy-only markets. We study the long-term capacity expansion decision in fossil fuel and renewable technologies when electricity demand is uncertain. We model a relevant tradeoff: a higher share of renewable production can be priced at the higher marginal cost of fossil fuel production, yet the likelihood of achieving higher profits is reduced because more electricity demand is met by cheaper renewable production. We illustrate our theoretical results comparing the optimal solutions under a business- as-usual scenario and under an ETS scenario. This illustration shows under which limiting market settings a monopolist prefers to withhold investments in renewable energy sources, highlighting the potential distortionary effect introduced via an ETS. Our conclusions remain unaltered under varying key modelling assumptions

Relevant States and Memory in Markov Chain Bootstrapping and Simulation

Markov chain theory is proving to be a powerful approach to bootstrap highly nonlinear time series. In this work we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular the choice of memory lags and the aggregation of irrelevant states are obtained by looking for regularities in the transition probabilities. Our approach is based on an optimization model. More specifically we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping: preserving the “structural” similarity between the original and the simulated series and assuring a controlled diversification of the latter. A discussion based on information theory is developed to define the desirable properties for such optimal criteria. Two numerical tests are developed to verify the effectiveness of the method proposed here

Relevant States and Memory in Markov Chain Bootstrapping and Simulation

Markov chain theory is proving to be a powerful approach to bootstrap highly nonlinear time series. In this work we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular the choice of memory lags and the aggregation of irrelevant states are obtained by looking for regularities in the transition probabilities. Our approach is based on an optimization model. More specifically we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping: preserving the “structural” similarity between the original and the simulated series and assuring a controlled diversification of the latter. A discussion based on information theory is developed to define the desirable properties for such optimal criteria. Two numerical tests are developed to verify the effectiveness of the method proposed here