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Kirsten Ralf - One of the best experts on this subject based on the ideXlab platform.
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The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks
Economics Bulletin, 2020Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:With non-controllable auto-regressive shocks, the welfare of Ramsey Optimal Policy is the solution of a single Riccati equation of a linear quadratic regulator. The existing theory by Hansen and Sargent (2007) refers to an additional Sylvester equation but miss another equation for computing the block matrix weighting the square of non-controllable variables in the welfare function. There is no need to simulate impulse response functions over a long period, to compute period loss functions and to sum their discounted value over this long period, as currently done so far. Welfare is computed for the case of the new-Keynesian Phillips curve with an auto-regressive cost-push shock. JEL classi…cation numbers: C61, C62, C73, E47, E52, E61, E63.
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The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks
2020Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:With non-controllable auto-regressive shocks, the welfare of Ramsey Optimal Policy is the solution of a single Riccati equation of a linear quadratic regulator. The existing theory by Hansen and Sargent (2007) refers to an additional Sylvester equation but miss another equation for computing the block matrix weighting the square of non-controllable variables in the welfare function. There is no need to simulate impulse response functions over a long period, to compute period loss functions and to sum their discounted value over this long period, as currently done so far. Welfare is computed for the case of the new-Keynesian Phillips curve with an auto-regressive cost-push shock.
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Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy
2020Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:This paper compares different implementations of monetary Policy in a new- Keynesian setting. We can show that a shift from Ramsey Optimal Policy under short term commitment (based on a negative-feed back mechanism) to a Taylor rule (based on a positive-feed back mechanism) corresponds to a Hopfbifurcation with opposite Policy advice and a change of the dynamic properties. This bifurcation occurs because of the ad hoc assumption that interest rate is a forward-looking variable when Policy targets (inflation and out put gap) a reforward-looking variables in the new-Keynesian theory.
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Ramsey Optimal Policy in theNew-Keynesian Model with Public Debt
Macroeconomic Dynamics, 2020Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:In the discrete-time new-Keynesian model with public debt, Ramsey Optimal Policy eliminates the indeterminacy of simple-rules multiple equilibria between the fiscal theory of the price level versus new-Keynesian versus an unpleasant equilibrium. If public debt volatility is taken into account into the loss function, the interest rate responds to public debt besides inflation and output gap. Else, the Taylor rule is identical to Ramsey Optimal Policy when there is zero public debt. The Optimal fiscal-rule parameter implies the local stability of public-debt dynamics (“passive” fiscal Policy).
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Ramsey Optimal Policy in the New-Keynesian Model with Public Debt
2019Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:This paper compares Ramsey Optimal Policy for the new-Keynesian model with public debt with its .scal theory of the price level (FTPL) equilibrium. Both the fiscal theory of the price level and Ramsey Optimal Policy implies that a de.cit shock is instantaneously followed by an increase of in.ation and output gap. But each Optimal Policy parameters belongs in di¤erent sets with respect to FTPL. The Optimal .scal rule parameter implies local stability of public debt dynamics ("passive fiscal Policy"). The Optimal Taylor rule parameter for in.ation is larger than one. The Optimal Taylor rule parameter for output gap is negative, because of the intertemporal substitution e¤ect of interest rate on output gap. Both Taylor rule Optimal parameters implies the local stability of inflation and output gap dynamics.
Jean-bernard Chatelain - One of the best experts on this subject based on the ideXlab platform.
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The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks
Economics Bulletin, 2020Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:With non-controllable auto-regressive shocks, the welfare of Ramsey Optimal Policy is the solution of a single Riccati equation of a linear quadratic regulator. The existing theory by Hansen and Sargent (2007) refers to an additional Sylvester equation but miss another equation for computing the block matrix weighting the square of non-controllable variables in the welfare function. There is no need to simulate impulse response functions over a long period, to compute period loss functions and to sum their discounted value over this long period, as currently done so far. Welfare is computed for the case of the new-Keynesian Phillips curve with an auto-regressive cost-push shock. JEL classi…cation numbers: C61, C62, C73, E47, E52, E61, E63.
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The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks
2020Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:With non-controllable auto-regressive shocks, the welfare of Ramsey Optimal Policy is the solution of a single Riccati equation of a linear quadratic regulator. The existing theory by Hansen and Sargent (2007) refers to an additional Sylvester equation but miss another equation for computing the block matrix weighting the square of non-controllable variables in the welfare function. There is no need to simulate impulse response functions over a long period, to compute period loss functions and to sum their discounted value over this long period, as currently done so far. Welfare is computed for the case of the new-Keynesian Phillips curve with an auto-regressive cost-push shock.
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Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy
2020Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:This paper compares different implementations of monetary Policy in a new- Keynesian setting. We can show that a shift from Ramsey Optimal Policy under short term commitment (based on a negative-feed back mechanism) to a Taylor rule (based on a positive-feed back mechanism) corresponds to a Hopfbifurcation with opposite Policy advice and a change of the dynamic properties. This bifurcation occurs because of the ad hoc assumption that interest rate is a forward-looking variable when Policy targets (inflation and out put gap) a reforward-looking variables in the new-Keynesian theory.
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Ramsey Optimal Policy in theNew-Keynesian Model with Public Debt
Macroeconomic Dynamics, 2020Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:In the discrete-time new-Keynesian model with public debt, Ramsey Optimal Policy eliminates the indeterminacy of simple-rules multiple equilibria between the fiscal theory of the price level versus new-Keynesian versus an unpleasant equilibrium. If public debt volatility is taken into account into the loss function, the interest rate responds to public debt besides inflation and output gap. Else, the Taylor rule is identical to Ramsey Optimal Policy when there is zero public debt. The Optimal fiscal-rule parameter implies the local stability of public-debt dynamics (“passive” fiscal Policy).
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Ramsey Optimal Policy in the New-Keynesian Model with Public Debt
2019Co-Authors: Jean-bernard Chatelain, Kirsten RalfAbstract:This paper compares Ramsey Optimal Policy for the new-Keynesian model with public debt with its .scal theory of the price level (FTPL) equilibrium. Both the fiscal theory of the price level and Ramsey Optimal Policy implies that a de.cit shock is instantaneously followed by an increase of in.ation and output gap. But each Optimal Policy parameters belongs in di¤erent sets with respect to FTPL. The Optimal .scal rule parameter implies local stability of public debt dynamics ("passive fiscal Policy"). The Optimal Taylor rule parameter for in.ation is larger than one. The Optimal Taylor rule parameter for output gap is negative, because of the intertemporal substitution e¤ect of interest rate on output gap. Both Taylor rule Optimal parameters implies the local stability of inflation and output gap dynamics.
Hao Xu - One of the best experts on this subject based on the ideXlab platform.
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Optimal Policy for software vulnerability disclosure
Management Science, 2008Co-Authors: Ashish Arora, Rahul Telang, Hao XuAbstract:Software vulnerabilities represent a serious threat to cybersecurity, most cyberattacks exploit known vulnerabilities. Unfortunately, there is no agreed-upon Policy for their disclosure. Disclosure Policy (which sets a protected period given to a vendor to release the patch for the vulnerability) indirectly affects the speed and quality of the patch that a vendor develops. Thus, CERT/CC and similar bodies acting in the public interest can use disclosure to influence the behavior of vendors and reduce social cost. This paper develops a framework to analyze the Optimal timing of disclosure. We formulate a model involving a social planner who sets the disclosure Policy and a vendor who decides on the patch release. We show that the vendor typically releases the patch less expeditiously than is socially Optimal. The social planner Optimally shrinks the protected period to push the vendor to deliver the patch more quickly, and sometimes the patch release time coincides with disclosure. We extend the model to allow the proportion of users implementing patches to depend upon the quality (chosen by the vendor) of the patch. We show that a longer protected period does not always result in a better patch quality. Another extension allows for some fraction of users to use “work-arounds.” We show that the possibility of work-arounds can provide the social planner with more leverage, and hence the social planner shrinks the protected period. Interestingly, the possibility of work-arounds can sometimes increase the social cost due to the negative externalities imposed by the users who are able to use the work-arounds on the users who are not.
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Optimal Policy for Software Vulnerability Disclosure
SSRN, 2005Co-Authors: Ashish Arora, Rahul Telang, Hao XuAbstract:Software vulnerabilities represent a serious threat to cyber security: most cyber-attacks exploit known vulnerabilities. Unfortunately, there is no agreed-upon Policy for their disclosure. Disclosure Policy (protected period given to a vendor to patch the vulnerability) indirectly affects the speed and quality of the patch that a vendor develops. Thus CERT/CC and similar bodies acting in the public interest can use it to influence behavior of vendors and reduce social cost. This paper develops a framework to analyze the Optimal timing of disclosure Policy. We formulate a game-theoretic model involving a social planner who sets disclosure Policy and a vendor who decides on patching. We show that vendors (almost) always patch less expeditiously than is socially Optimal. The social planner Optimally shrinks the protected period to push vendors to deliver the patch more quickly. We extend the basic model to allow the proportion of users implementing patches to depend upon the quality (chosen by the vendor) of the patch. Another extension allows for some fraction of users to use \work-arounds. While the basic results of our model are robust, these extension provide additional insights into how disclosure Policy affects a vendor's decision and, in turn, what should a Policy-maker do.
Ashish Arora - One of the best experts on this subject based on the ideXlab platform.
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Optimal Policy for software vulnerability disclosure
Management Science, 2008Co-Authors: Ashish Arora, Rahul Telang, Hao XuAbstract:Software vulnerabilities represent a serious threat to cybersecurity, most cyberattacks exploit known vulnerabilities. Unfortunately, there is no agreed-upon Policy for their disclosure. Disclosure Policy (which sets a protected period given to a vendor to release the patch for the vulnerability) indirectly affects the speed and quality of the patch that a vendor develops. Thus, CERT/CC and similar bodies acting in the public interest can use disclosure to influence the behavior of vendors and reduce social cost. This paper develops a framework to analyze the Optimal timing of disclosure. We formulate a model involving a social planner who sets the disclosure Policy and a vendor who decides on the patch release. We show that the vendor typically releases the patch less expeditiously than is socially Optimal. The social planner Optimally shrinks the protected period to push the vendor to deliver the patch more quickly, and sometimes the patch release time coincides with disclosure. We extend the model to allow the proportion of users implementing patches to depend upon the quality (chosen by the vendor) of the patch. We show that a longer protected period does not always result in a better patch quality. Another extension allows for some fraction of users to use “work-arounds.” We show that the possibility of work-arounds can provide the social planner with more leverage, and hence the social planner shrinks the protected period. Interestingly, the possibility of work-arounds can sometimes increase the social cost due to the negative externalities imposed by the users who are able to use the work-arounds on the users who are not.
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Optimal Policy for Software Vulnerability Disclosure
SSRN, 2005Co-Authors: Ashish Arora, Rahul Telang, Hao XuAbstract:Software vulnerabilities represent a serious threat to cyber security: most cyber-attacks exploit known vulnerabilities. Unfortunately, there is no agreed-upon Policy for their disclosure. Disclosure Policy (protected period given to a vendor to patch the vulnerability) indirectly affects the speed and quality of the patch that a vendor develops. Thus CERT/CC and similar bodies acting in the public interest can use it to influence behavior of vendors and reduce social cost. This paper develops a framework to analyze the Optimal timing of disclosure Policy. We formulate a game-theoretic model involving a social planner who sets disclosure Policy and a vendor who decides on patching. We show that vendors (almost) always patch less expeditiously than is socially Optimal. The social planner Optimally shrinks the protected period to push vendors to deliver the patch more quickly. We extend the basic model to allow the proportion of users implementing patches to depend upon the quality (chosen by the vendor) of the patch. Another extension allows for some fraction of users to use \work-arounds. While the basic results of our model are robust, these extension provide additional insights into how disclosure Policy affects a vendor's decision and, in turn, what should a Policy-maker do.
Zhihua Zhang - One of the best experts on this subject based on the ideXlab platform.
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Finding the Near Optimal Policy via Adaptive Reduced Regularization in MDPs.
arXiv: Learning, 2020Co-Authors: Wenhao Yang, Guangzeng Xie, Zhihua ZhangAbstract:Regularized MDPs serve as a smooth version of original MDPs. However, biased Optimal Policy always exists for regularized MDPs. Instead of making the coefficient{\lambda}of regularized term sufficiently small, we propose an adaptive reduction scheme for {\lambda} to approximate Optimal Policy of the original MDP. It is shown that the iteration complexity for obtaining an{\epsilon}-Optimal Policy could be reduced in comparison with setting sufficiently small{\lambda}. In addition, there exists strong duality connection between the reduction method and solving the original MDP directly, from which we can derive more adaptive reduction method for certain algorithms.
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A Regularized Approach to Sparse Optimal Policy in Reinforcement Learning
arXiv: Machine Learning, 2019Co-Authors: Wenhao Yang, Zhihua ZhangAbstract:We propose and study a general framework for regularized Markov decision processes (MDPs) where the goal is to find an Optimal Policy that maximizes the expected discounted total reward plus a Policy regularization term. The extant entropy-regularized MDPs can be cast into our framework. Moreover, under our framework, many regularization terms can bring multi-modality and sparsity, which are potentially useful in reinforcement learning. In particular, we present sufficient and necessary conditions that induce a sparse Optimal Policy. We also conduct a full mathematical analysis of the proposed regularized MDPs, including the Optimality condition, performance error, and sparseness control. We provide a generic method to devise regularization forms and propose off-Policy actor critic algorithms in complex environment settings. We empirically analyze the numerical properties of Optimal policies and compare the performance of different sparse regularization forms in discrete and continuous environments.
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NeurIPS - A Regularized Approach to Sparse Optimal Policy in Reinforcement Learning
2019Co-Authors: Wenhao Yang, Zhihua ZhangAbstract:We propose and study a general framework for regularized Markov decision processes (MDPs) where the goal is to find an Optimal Policy that maximizes the expected discounted total reward plus a Policy regularization term. The extant entropy-regularized MDPs can be cast into our framework. Moreover, under our framework, many regularization terms can bring multi-modality and sparsity, which are potentially useful in reinforcement learning. In particular, we present sufficient and necessary conditions that induce a sparse Optimal Policy. We also conduct a full mathematical analysis of the proposed regularized MDPs, including the Optimality condition, performance error, and sparseness control. We provide a generic method to devise regularization forms and propose off-Policy actor critic algorithms in complex environment settings. We empirically analyze the numerical properties of Optimal policies and compare the performance of different sparse regularization forms in discrete and continuous environments.
