A Note on Equity Premia in Markets with Heterogeneous Agents

We analyze a static partial equilibrium model where the agents are not only heterogeneous in their beliefs about the return on risky assets but also in their attitude to it. While some agents in the economy are subjective utility maximizers others behave ambiguity averse in the sense of Knight (1921). If ambiguity averse agents meet overly optimistic subjective utility maximizers in the market lower equity premia can arise in the equilibrium than in a purely subjective utility framework.Ambiguity, Partial Equilibrium, Heterogeneous Agents, No-Trade Interval

Exercise Strategies for American Exotic Options under Ambiguity

We analyze several exotic options of American style in a multiple prior setting and study the optimal exercise strategy from the perspective of an ambiguity averse buyer in a discrete time model of Cox–Ross–Rubinstein style. The multiple prior model relaxes the assumption of a known distribution of the stock price process and takes into account decision maker’s inability to completely determine the underlying asset’s price dynamics. In order to evaluate the American option the decision maker needs to solve a stopping problem. Unlike the classical approach ambiguity averse decision maker uses a class of measures to evaluate her expected payoffs instead of a unique prior. Given time-consistency of the set of priors an appropriate version of backward induction leads to the solution as in the classical case. Using a duality result the multiple prior stopping problem can be related to the classical stopping problem for a certain probability measure – the worst-case measure. Therefore, the problem can be reduced to identifying the worst-case measure. We obtain the form of the worstcase measure for different classes of exotic options explicitly exploiting the observation that the options can be decomposed in simpler event-driven claims.American option, optimal stopping, ambiguity, uncertainty aversion

The Best Choice Problem under ambiguity

We model and solve Best Choice Problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. The decision faces ambiguity about the probability that a candidate a relatively top applicant is actually best among all applicants. We show that our model covers the classical secretary problem, but also other interesting classes of problems. We provide a closed form solution of the problem for time-consistent priors using minimax backward induction. As in the classical case the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule.Best Choice Problem

A Note on Equity Premia in Markets with Heterogeneous Agents

Chudjakow T. A Note on Equity Premia in Markets with Heterogeneous Agents. Working Papers. Institute of Mathematical Economics. Vol 444. Bielefeld: Center for Mathematical Economics; 2011.We analyze a static partial equilibrium model where the agents are not only heterogeneous in their beliefs about the return on risky assets but also in their attitude to it. While some agents in the economy are subjective utility maximizers others behave ambiguity averse in the sense of Knight (1921). If ambiguity averse agents meet overly optimistic subjective utility maximizers in the market lower equity premia can arise in the equilibrium than in a purely subjective utility framework

On Knightian uncertainty models : optimal behavior in presence of model uncertainty

Chudjakow T. On Knightian uncertainty models : optimal behavior in presence of model uncertainty. Bielefeld (Germany): Bielefeld University; 2010.In the framework of Knightian uncertainty more precisely in the model introduced by Epstein and Schneider (2003) 3 different questions concerning the optimal behavior in presence of ambiguity are studied. The first part reformulates and solves Best Choice Problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. It shows that as in the classical case the derived stopping strategy is simple. However, ambiguity can lead to substantial differences to the classical threshold rule leading to later or earlier stopping. Second part analyzes several exotic options of American style in a multiple prior setting. It studies the optimal exercise strategy from the perspective of an ambiguity averse buyer in a discrete market model. The section provides the explicit form of worst-case measure for different classes of exotic options exploiting the observation that the options can be decomposed in simpler event-driven claims. The last part analyzes a static partial equilibrium model where the agents are not only heterogeneous in their beliefs about the return on risky assets but also in their attitude to it. While some agents in the economy are subjective utility maximizers others behave ambiguity averse in the sense of Knight (1921). If ambiguity averse agents meet overly optimistic subjective utility maximizers in the market lower equity premia can arise in the equilibrium than in a purely subjective utility framework

The Best Choice Problem under Ambiguity

Chudjakow T, Riedel F. The Best Choice Problem under Ambiguity. Working Papers. Institute of Mathematical Economics. Vol 413. Bielefeld: Universität Bielefeld; 2009.We model and solve Best Choice Problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. The decision faces ambiguity about the probability that a candidate - a relatively top applicant - is actually best among all applicants. We show that our model covers the classical secretary problem, but also other interesting classes of problems. We provide a closed form solution of the problem for time-consistent priors using minimax backward induction. As in the classical case the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule

Exercise strategies for American exotic options under ambiguity

Chudjakow T, Vorbrink J. Exercise strategies for American exotic options under ambiguity. Working Papers. Institute of Mathematical Economics. Vol 421. Bielefeld: Universität Bielefeld; 2009.We analyze several exotic options of American style in a multiple prior setting and study the optimal exercise strategy from the perspective of an ambiguity averse buyer in a discrete time model of Cox-Ross-Rubinstein style. The multiple prior model relaxes the assumption of a known distribution of the stock price process and takes into account decision maker's inability to completely determine the underlying asset's price dynamics. In order to evaluate the American option the decision maker needs to solve a stopping problem. Unlike the classical approach ambiguity averse decision maker uses a class of measures to evaluate her expected payoffs instead of a unique prior. Given time-consistency of the set of priors an appropriate version of backward induction leads to the solution as in the classical case. Using a duality result the multiple prior stopping problem can be related to the classical stopping problem for a certain probability measure - the worst-case measure. Therefore, the problem can be reduced to identifying the worst-case measure. We obtain the form of the worst-case measure for different classes of exotic options explicitly exploiting the observation that the option can be decomposed in simpler event-driven claims

The best choice problem under ambiguity

Chudjakow T, Riedel F. The best choice problem under ambiguity. Economic Theory. 2013;54(1):77-97