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Raymond Kan - One of the best experts on this subject based on the ideXlab platform.
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a new variance bound on the stochastic Discount Factor
The Journal of Business, 2006Co-Authors: Raymond Kan, Guofu ZhouAbstract:In this paper, we construct a new variance bound on any stochastic Discount Factor (SDF) of the form \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $m=m( x) $ \end{document} , with x being a vector of state variables, which tightens the well‐known Hansen‐Jagannathan bound by a ratio of one over the multiple correlation coefficient between x and the standard minimum variance SDF, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepack...
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gmm tests of stochastic Discount Factor models with useless Factors
Journal of Financial Economics, 1999Co-Authors: Raymond Kan, Chu ZhangAbstract:Abstract This paper studies generalized method of moments tests for the stochastic Discount Factor representation of asset pricing models when one of the proposed Factors is in fact useless, defined as being independent of the asset returns. Analytic results on asymptotic distributions and simulation results on finite sample distributions both show that (i) the Wald test tends to overreject the hypothesis of a zero Factor premium for a useless Factor when the model is misspecified, (ii) with the presence of a useless Factor, the power of the over-identifying restriction test in rejecting misspecified models is reduced, and in some cases a misspecified model with a useless Factor is more likely to be accepted than the true model.
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a critique of the stochastic Discount Factor methodology
Journal of Finance, 1999Co-Authors: Raymond Kan, Guofu ZhouAbstract:In this paper, we point out that the widely used stochastic Discount Factor ~SDF! methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear Factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology. ASSET PRICING THEORIES, such as those of Sharpe ~1964!, Lintner ~1965!, Black ~1972!, Merton ~1973!, Ross ~1976!, and Breeden ~1979!, show that the expected return on a financial asset is a linear function of its covariances ~or betas! with some systematic risk Factors. This implication has been tested extensively in the finance literature by the so-called “traditional methodologies.” In the traditional methodologies, a data-generating process is first proposed for the returns, and then the restrictions imposed by an asset pricing model are tested as parametric constraints on the return-generating process. The approach taken by the traditional methodologies has a potential problem, which is that when the proposed return-generating process is misspecified the test results could be misleading. Therefore, in applying the traditional methodologies, researchers typically have to justify that the proposed data-generating process provides a good description of the returns. For example, when the proposed return-generating process is a Factor model, one would like the model to have high R 2 in explaining the returns on the test assets, especially when the test assets are well-diversified portfolios. As many of the earlier theories are special cases of the stochastic Discount Factor ~SDF! model, recent empirical asset pricing studies have been focused on testing the pricing restrictions in terms of the SDF model, rather
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A critique of the stochastic Discount Factor methodology
The Journal of Finance, 1999Co-Authors: Raymond Kan, Guofu ZhouAbstract:In this paper, we point out that the widely used stochastic Discount Factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear Factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology. Copyright The American Finance Association 1999.
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a critique of the stochastic Discount Factor methodology
1999Co-Authors: Raymond Kan, Guofu ZhouAbstract:In this paper, we point out that the widely used stochastic Discount Factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear Factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology.
Silviu Pitis - One of the best experts on this subject based on the ideXlab platform.
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rethinking the Discount Factor in reinforcement learning a decision theoretic approach
National Conference on Artificial Intelligence, 2019Co-Authors: Silviu PitisAbstract:Reinforcement learning (RL) agents have traditionally been tasked with maximizing the value function of a Markov decision process (MDP), either in continuous settings, with fixed Discount Factor γ
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AAAI - Rethinking the Discount Factor in Reinforcement Learning: A Decision Theoretic Approach
Proceedings of the AAAI Conference on Artificial Intelligence, 2019Co-Authors: Silviu PitisAbstract:Reinforcement learning (RL) agents have traditionally been tasked with maximizing the value function of a Markov decision process (MDP), either in continuous settings, with fixed Discount Factor γ
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rethinking the Discount Factor in reinforcement learning a decision theoretic approach
arXiv: Learning, 2019Co-Authors: Silviu PitisAbstract:Reinforcement learning (RL) agents have traditionally been tasked with maximizing the value function of a Markov decision process (MDP), either in continuous settings, with fixed Discount Factor $\gamma < 1$, or in episodic settings, with $\gamma = 1$. While this has proven effective for specific tasks with well-defined objectives (e.g., games), it has never been established that fixed Discounting is suitable for general purpose use (e.g., as a model of human preferences). This paper characterizes rationality in sequential decision making using a set of seven axioms and arrives at a form of Discounting that generalizes traditional fixed Discounting. In particular, our framework admits a state-action dependent "Discount" Factor that is not constrained to be less than 1, so long as there is eventual long run Discounting. Although this broadens the range of possible preference structures in continuous settings, we show that there exists a unique "optimizing MDP" with fixed $\gamma < 1$ whose optimal value function matches the true utility of the optimal policy, and we quantify the difference between value and utility for suboptimal policies. Our work can be seen as providing a normative justification for (a slight generalization of) Martha White's RL task formalism (2017) and other recent departures from the traditional RL, and is relevant to task specification in RL, inverse RL and preference-based RL.
Timothy M Christensen - One of the best experts on this subject based on the ideXlab platform.
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nonparametric stochastic Discount Factor decomposition
Econometrica, 2017Co-Authors: Timothy M ChristensenAbstract:Stochastic Discount Factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron–Frobenius eigenfunction problem of Hansen and Scheinkman, 2009. Our empirical framework allows researchers to (i) construct time series of the estimated permanent and transitory components and (ii) estimate the yield and the change of measure which characterize pricing over long investment horizons. We also introduce nonparametric estimators of the continuation value function in a class of models with recursive preferences by reinterpreting the value function recursion as a nonlinear Perron–Frobenius problem. We establish consistency and convergence rates of the eigenfunction estimators and asymptotic normality of the eigenvalue estimator and estimators of related functionals. As an application, we study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics.
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nonparametric stochastic Discount Factor decomposition
2015Co-Authors: Timothy M ChristensenAbstract:We introduce econometric methods to perform estimation and inference on the permanent and transitory components of the stochastic Discount Factor (SDF) in dynamic Markov environments. The approach is nonparametric in that it does not impose parametric restrictions on the law of motion of the state process. We propose sieve estimators of the eigenvalue-eigenfunction pair which are used to decompose the SDF into its permanent and transitory components, as well as estimators of the long-run yield and the entropy of the permanent component of the SDF, allowing for a wide variety of empirically relevant setups. Consistency and convergence rates are established. The estimators of the eigenvalue, yield and entropy are shown to be asymptotically normal and semiparametrically efficient when the SDF is observable. We also introduce nonparametric estimators of the continuation value under Epstein-Zin preferences, thereby extending the scope of our estimators to an important class of recursive preferences. The estimators are simple to implement, perform favorably in simulations, and may be used to numerically compute the eigenfunction and its eigenvalue in fully specified models when analytical solutions are not available.
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nonparametric stochastic Discount Factor decomposition
arXiv: Methodology, 2014Co-Authors: Timothy M ChristensenAbstract:Stochastic Discount Factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009). Our empirical framework allows researchers to (i) recover the time series of the estimated permanent and transitory components and (ii) estimate the yield and the change of measure which characterize pricing over long investment horizons. We also introduce nonparametric estimators of the continuation value function in a class of models with recursive preferences by reinterpreting the value function recursion as a nonlinear Perron-Frobenius problem. We establish consistency and convergence rates of the eigenfunction estimators and asymptotic normality of the eigenvalue estimator and estimators of related functionals. As an application, we study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics.
Javed Iqbal - One of the best experts on this subject based on the ideXlab platform.
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estimation of Discount Factor and coecient of relative risk aversion in selected countries
2012Co-Authors: Waqas Ahmed, Adnan Haider, Javed IqbalAbstract:We estimate the long-run Discount Factor for a group of developed and de- veloping countries through standard methodology incorporating adaptive expectations of ination. We nd that the Discount Factor of developing countries is relatively nearer to unity as compared to that of the developed countries. In the second part, while consider- ing a standard Euler equation for household's intertemporal consumption, we estimate the parameter of constant relative risk aversion (CRRA) for Pakistan by using the Generalized Method of Moments (GMM) approach. The resulting parameter value of CRRA conrms to the empirical range for developing countries (as given in, Cardenas and Carpenter, 2008). The GMM estimator for the Discount Factor reinforces its result from the rst part of the paper. Consequently we show that dierent combination values for both the parameters
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Estimation of Discount Factor ß and Coefficient of Relative Risk Aversion ? in Selected Countries
2012Co-Authors: Waqas Ahmed, Adnan Haider, Javed IqbalAbstract:The long-run Discount Factor for a group of developed and developing countries is estimated through standard methodology incorporating adaptive expectations of inflation. In the second part, while considering a standard Euler equation for household's intertemporal consumption, the parameter of constant relative risk aversion (CRRA) for Pakistan is estimated by using the Generalized Method of Moments (GMM) approach. The resulting parameter value of CRRA conforms to the empirical range for developing countries (as given in, Cardenas and Carpenter, 2008) The GMM estimator for the Discount Factor reinforces its result from the first part of the paper. [SBP WP no. 53]. URL:[http://www.sbp.org.pk/publications/wpapers/2012/wp53.pdf].
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Estimation of Discount Factor (beta) and coefficient of relative risk aversion (gamma) in selected countries
2012Co-Authors: Waqas Ahmed, Adnan Haider, Javed IqbalAbstract:We estimate the long-run Discount Factor for a group of developed and developing countries through standard methodology incorporating adaptive expectations of inflation. We find that the Discount Factor of developing countries is relatively nearer to unity as compared to that of the developed countries. In the second part, while considering a standard Euler equation for household's intertemporal consumption, we estimate the parameter of constant relative risk aversion (CRRA) for Pakistan by using the Generalized Method of Moments (GMM) approach. The resulting parameter value of CRRA confirms to the empirical range for developing countries (as given in, Cardenas and Carpenter, 2008). The GMM estimator for the Discount Factor reinforces its result from the first part of the paper. Consequently we show that different combination values for both the parameters result in different (in terms of magnitude) impulse response functions, in response to tight monetary policy shocks in a simple New Keynesian macroeconomic model.
Jie Zhang - One of the best experts on this subject based on the ideXlab platform.
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an ewma algorithm with a cycled resetting cr Discount Factor for drift and fault of high mix run to run control
IEEE Transactions on Industrial Informatics, 2010Co-Authors: Y. Zheng, David Shanhill Wong, Shishang Jang, Yanwei Wang, Jie ZhangAbstract:Run-to-run controllers based on the exponential weighted moving average (EWMA) statistic are probably the most frequently used for the quality control of certain semiconductor manufacturing process steps. The threaded-EWMA run-to-run control is an important stable control scheme. However, the process outputs will deviate largely in the first few runs of each cycle if the disturbance follows an IMA(1,1) series with deterministic linear drift and the thread has a long break length. In this paper, the output of the threaded-EWMA run-to-run control is derived, stability conditions are given, and the causes of large deviations in the first few runs of each cycle are found. Based on the analysis of system performance, a cycled resetting (CR) algorithm for Discount Factor is proposed to reduce the large deviations, as well as to achieve the minimum asymptotic variance control. Furthermore, how to deal with step fault is also discussed in this paper. By analyzing the influence of the fault, a Discount Factor resetting fault-tolerant (RFT) approach is proposed. Simulation study shows both the mean square error (MSE) and variance of the output by the proposed algorithm is about 30% to 50% lower than that of the algorithm with fixed Discount Factor in the process with and without oscillation. This verifies the effectiveness of the proposed approach.