By Lars Peter Hansen, Thomas J Sargent
Uncertainty inside monetary types is a set of papers adapting and making use of strong regulate concept to difficulties in economics and finance. This e-book extends rational expectancies versions via together with brokers who doubt their types and undertake precautionary judgements designed to guard themselves from adversarial results of version misspecification. This habit has effects for what are mostly interpreted as marketplace costs of danger, yet large components of which may still truly be interpreted as industry costs of version uncertainty. The chapters talk about methods of calibrating brokers' fears of version misspecification in quantitative contexts.
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In Jacobson (1973), the problem is formulated for the undiscounted case. Contributions Bouakiz and Sobel (1985) and Whittle (1990) described how recursions on a Riccati diﬀerence equation apply to a discounted version of the problem. In their formulation with discounting, the optimal decision rules fail to be time-invariant: over time the eﬀects of the risk-parameter “wear oﬀ,” and the decision rules eventually converge to what would prevail in the usual linear-quadratic case. We propose an alternative discounted version of the problem that preserves time-invariance of the decision rules in the inﬁnite-horizon problem.
E(·|JT −1 ) as well. 2) has the features that: (1) the value functions are quadratic functions of the state vector, as in the familiar optimal linear regulator problem and in its risk-adjusted version suggested by Jacobson (1973) and Whittle (1981); (2) the statistics of the noise process inﬂuence the optimal decision rules in a way that depends on the value of σ; and (3) the inﬁnite time horizon problem is well posed and yields a timeinvariant optimal linear control law. 2 Cost Recursions and Aggregator Functions To characterize some properties of our discounted, risk-adjusted costs we follow Koopmans (1960), Kreps and Porteus (1978), Lucas and Stokey (1984), Epstein and Zin (1989) and use an aggregator function α to represent costs recursively.
All of this means that for the linear-quadratic-Gaussian case, replacing E with T in the Bellman equation associated with the dynamic programming problem typically used in ﬁnance or macroeconomics creates no additional analytical challenges. With our eyes on applications in macroeconomics and ﬁnance, we incorporate discounting diﬀerently than Whittle (1989a, 1990). Whittle eﬀectively discounts future time t contributions to utilities, but does not discount future contributions to entropy. A consequence of that is to render decision rules time-dependent in a way that makes eﬀects from risk-sensitivity and concerns about model speciﬁcation wear oﬀ with the passage of time, a feature that we do not like for many applications.