arXiv subjects

Larry G. Epstein

Publications and source records attributed to Larry G. Epstein.

5 recordsLinked to original sources

arXiv2023

Approximate optimality and the risk/reward tradeoff in a class of bandit problems

This paper studies a sequential decision problem where payoff distributions are known and where the riskiness of payoffs matters. Equivalently, it studies sequential choice from a repeated set of independent lotteries. The decision-maker is assumed to pursue strategies that are approximately optimal for large horizons. By exploiting the tractability afforded by asymptotics, conditions are derived characterizing when specialization in one action or lottery throughout is asymptotically optimal and when optimality requires intertemporal diversification. The key is the constancy or variability of risk attitude. The main technical tool is a new central limit theorem.

econ.TH↗

arXiv2022

A Central Limit Theorem, Loss Aversion and Multi-Armed Bandits

This paper studies a multi-armed bandit problem where the decision-maker is loss averse, in particular she is risk averse in the domain of gains and risk loving in the domain of losses. The focus is on large horizons. Consequences of loss aversion for asymptotic (large horizon) properties are derived in a number of analytical results. The analysis is based on a new central limit theorem for a set of measures under which conditional variances can vary in a largely unstructured history-dependent way subject only to the restriction that they lie in a fixed interval.

math.PR↗

arXiv2020

A Central Limit Theorem for Sets of Probability Measures

We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is) defined by a backward stochastic differential equation that can be interpreted as modeling an ambiguous continuous-time random walk.

math.PR↗

arXiv2017

Optimal Learning under Robustness and Time-Consistency

We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed-form, with a focus on two specific settings: Ellsberg's two-urn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is studied.

econ.GN↗

arXiv2013

Ambiguous volatility and asset pricing in continuous time

This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments. Ambiguous volatility implies market incompleteness that rules out perfect hedging. Consequently, hedging arguments determine prices only up to intervals. However, sharper predictions can be obtained by assuming preference maximization and equilibrium. Thus we apply the model of utility to a representative agent endowment economy to study equilibrium asset returns. A version of the C-CAPM is derived and the effects of ambiguous volatility are described.

q-fin.PR↗