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Robustness and ambiguity in continuous time

Lars Peter Hansen, Thomas J. Sargent
2011 Journal of Economic Theory  
We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity.  ...  Two continuous-time formulations are counterparts of two discrete-time recursive specifications of [16] . One formulation shares features of the smooth ambiguity model of [24, 25] .  ...  When we follow [25] and use U * in (18) and expected utility over second-order acts, the ambiguity adjustment vanishes in the continuous time limit computed in subsection 8.1.  ... 
doi:10.1016/j.jet.2011.01.004 fatcat:5vjp266hsraclicgqkufddj7ri

Aversion to ambiguity and model misspecification in dynamic stochastic environments

Lars Peter Hansen, Jianjun Miao
2018 Proceedings of the National Academy of Sciences of the United States of America  
These recursive representations imply continuous time limiting Hamilton-Jacobi-Bellman equations for solving control problems in the presence of uncertainty. uncertainty | robustness | misspecification  ...  By design, these discrete time environments have revealing continuous time limits.  ...  ways for robustness concerns to persist in a continuous time limiting specification.  ... 
doi:10.1073/pnas.1811243115 pmid:30154169 fatcat:d5wzcl75bfecjintc52q3qxjwy

Three Types of Ambiguity

Lars Peter Hansen, Thomas J. Sargent
2012 Social Science Research Network  
For each of three types of ambiguity, we compute a robust Ramsey plan and an associated worst-case probability model.  ...  To reduce the dimension of the state in a recursive formulation, we transform the commitment multiplier to accommodate the heterogeneous beliefs that arise with ambiguity of types II and III.  ...  We begin by describing the model and Ramsey problems without ambiguity in discrete time and in continuous time. Let time be discrete with t = j for > 0 and integer j ≥ 0.  ... 
doi:10.2139/ssrn.2079787 fatcat:upsoqchfqbhp7e4rczumbtgtoq

Three types of ambiguity

Lars Peter Hansen, Thomas J. Sargent
2012 Journal of Monetary Economics  
For each of three types of ambiguity, we compute a robust Ramsey plan and an associated worst-case probability model.  ...  To reduce the dimension of the state in a recursive formulation, we transform the commitment multiplier to accommodate the heterogeneous beliefs that arise with ambiguity of types II and III.  ...  We begin by describing the model and Ramsey problems without ambiguity in discrete time and in continuous time. Let time be discrete with t = j for > 0 and integer j ≥ 0.  ... 
doi:10.1016/j.jmoneco.2012.06.003 fatcat:6mavr6vlszhgvodzuckjptkzpe

Foreword to the special issue on "Robustness, Knightian uncertainty, and games in finance"

Frank Riedel, Chris Shannon, Jan Werner
2017 Mathematics and Financial Economics  
At the same time, due in part to the financial crisis starting in 2007, the need for "robust finance" became clear both in practice and in theory, and since then robust finance has become one of the main  ...  In recent years, the related issues of Knightian uncertainty and robustness have emerged as major themes in financial economics and decision theory.  ...  under Knightian uncertainty, both in discrete and continuous time.  ... 
doi:10.1007/s11579-017-0208-x fatcat:dyhh2dc3g5hg7kzy7f3mkcwrqm

Robust Contracts in Continuous Time

Jianjun Miao, Alejandro Rivera
2016 Econometrica  
We study two types of robust contracting problem under hidden action in continuous time.  ...  In type I problem, the principal is ambiguous about the project cash flows, while he is ambiguous about the agent's beliefs in type II problem.  ...  We shall focus on formulating and solving types I and II robust contracting problems in continuous time.  ... 
doi:10.3982/ecta13127 fatcat:zrnnc3ew3jf2nkuqj4f4vnrijq

A dynamic game approach to distributionally robust safety specifications for stochastic systems

Insoon Yang
2018 Automatica  
Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a desired set for all times, subject to the worst possible disturbance distribution in an ambiguity set  ...  This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances.  ...  The proposed distrbutionally robust safe policy maximizes the probability of a system remaining within a desired set for all times subject to the worst possible disturbance distribution in the ambiguity  ... 
doi:10.1016/j.automatica.2018.04.022 fatcat:bt4upct6nrhjvc2frtae6o3wuy

Introduction to model uncertainty and robustness

Lars Peter Hansen, Pascal Maenhout, Aldo Rustichini, Thomas J. Sargent, Marciano M. Siniscalchi
2006 Journal of Economic Theory  
This article introduces the symposium on model uncertainty and robustness.  ...  The paper also presents a new methodology for calculating detection-error probabilities in continuous-time models.  ...  in a robust way.  ... 
doi:10.1016/j.jet.2006.03.009 fatcat:ypsrzp6fg5hr3augwypx4qfrwi

Robust control of the multi-armed bandit problem

Felipe Caro, Aparupa Das Gupta
2015 Annals of Operations Research  
We study a robust model of the multi-armed bandit (MAB) problem in which the transition probabilities are ambiguous and belong to subsets of the probability simplex.  ...  We first show that for each arm there exists a robust counterpart of the Gittins index that is the solution to a robust optimal stopping-time problem and can be computed effectively with an equivalent  ...  Figure 3 : 3 Suboptimality Gap Table 1 : 1 Robust indices computational times in seconds (γ = 0.33) In order to study the effect of the discount factor δ we fix the ambiguity level β = 0.5 and the uncertainty  ... 
doi:10.1007/s10479-015-1965-7 fatcat:v2zyn6hazzafnhdeutsoubo3be

Precise Robust Positioning with Inertially Aided RTK

BRUNO M. SCHERZINGER
2006 Navigation  
The POS implements tightly coupled inertial/GPS integration with floated ambiguity estimation and fixed integer search in a single Kalman filter.  ...  A loosely coupled integration comprises the integration of inertial and GPS navigation solutions in a Kalman filter).  ...  A robust positioning and orientation system is needed to provide continuous and accurate vehicle position to the guidance subsystem.  ... 
doi:10.1002/j.2161-4296.2006.tb00374.x fatcat:zpceygoe2neixj7qgfa7aegjkq

Robust Control of the Multi-Armed Bandit Problem

Felipe Caro, Aparupa Das Gupta
2013 Social Science Research Network  
We study a robust model of the multi-armed bandit (MAB) problem in which the transition probabilities are ambiguous and belong to subsets of the probability simplex.  ...  We first show that for each arm there exists a robust counterpart of the Gittins index that is the solution to a robust optimal stopping-time problem and can be computed effectively with an equivalent  ...  Figure 3 : 3 Suboptimality Gap Table 1 : 1 Robust indices computational times in seconds (γ = 0.33) In order to study the effect of the discount factor δ we fix the ambiguity level β = 0.5 and the uncertainty  ... 
doi:10.2139/ssrn.2326583 fatcat:cziofb5o65dplksmnqrxduiutm

Distributional Robust Portfolio Construction based on Investor Aversion [article]

Xin Zhang
2022 arXiv   pre-print
Considering investors' aversion to loss and risk, and the ambiguous uncertainty characterizing asset returns, we construct a distributional robust portfolio model (DRP) under the condition that the distribution  ...  The distributional robust portfolio model considering aversion is empirically tested for superior performance in asset allocation, and we also compare common asset allocation strategies to further enhance  ...  The core of distributional robust optimization is in the construction of data-driven ambiguity set, where the random variables can be discrete or continuous.  ... 
arXiv:2203.13999v3 fatcat:sl3j3qvlznhmbebdm6m3ibujia

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Liyuan Wang, ,School of Mathematics and Statistics, Xi'an Jiaotong University, Shaanxi 710049, China, Zhiping Chen, Peng Yang, ,Center for Optimization Technique and Quantitative Finance, Xi'an International Academy for Mathematics and Mathematical Technology, Shaanxi 710049, China, ,School of Science, Xijing University, Xi'an, Shaanxi 710123, China
2017 Journal of Industrial and Management Optimization  
In this paper, we investigate the robust equilibrium control-measure policy for an ambiguity-averse and risk-averse fund manger under the mean-variance (MV) criterion.  ...  The ambiguity aversion is introduced by adopting the model uncertainty robustness framework developed by Anderson.  ...  The authors express their sincere gratitude to the editor and  ... 
doi:10.3934/jimo.2020018 fatcat:iq2z52xsj5fxhc2yk36o73ficq

Robustness and Ambiguity Aversion in General Equilibrium

Fabio Trojani, Paolo Vanini
2004 Social Science Research Network  
We study equilibria for two tractable wealth-homothetic settings of ambiguity aversion in continuous time. Such settings are motivated by a different robust control optimization problem.  ...  In general equilibrium, ambiguity aversion tends to induce a higher equilibrium equity premium and lower interest rates.  ...  time) and Anderson, Hansen and Sargent (AHS, 2003, in continuous time) .  ... 
doi:10.2139/ssrn.524685 fatcat:qyc6m6urdjhsloiq5x65awsbvy

Robustness and Ambiguity Aversion in General Equilibrium

Fabio Trojani, Paolo Vanini
2004 Review of Finance  
We study equilibria for two tractable wealth-homothetic settings of ambiguity aversion in continuous time. Such settings are motivated by a different robust control optimization problem.  ...  In general equilibrium, ambiguity aversion tends to induce a higher equilibrium equity premium and lower interest rates.  ...  time) and Anderson, Hansen and Sargent (AHS, 2003, in continuous time) .  ... 
doi:10.1023/b:eufi.0000035193.29969.40 fatcat:vtgpndljybcypdu6o2msk7nbtu
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