970 research outputs found
Optimal stopping under ambiguity
We consider optimal stopping problems for ambiguity averse decision makers with multiple priors. In general, backward induction fails. If, however, the class of priors is time-consistent, we establish a generalization of the classical theory of optimal stopping. To this end, we develop first steps of a martingale theory for multiple priors. We define minimax (super)martingales, provide a Doob-Meyer decomposition, and characterize minimax martingales. This allows us to extend the standard backward induction procedure to ambiguous, time-consistent preferences. The value function is the smallest process that is a minimax supermartingale and dominates the payoff process. It is optimal to stop when the current payoff is equal to the value function. Moving on, we study the infinite horizon case. We show that the value process satisfies the same backward recursion (Bellman equation) as in the finite horizon case. The finite horizon solutions converge to the infinite horizon solution. Finally, we characterize completely the set of time-consistent multiple priors in the binomial tree. We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).optimal stopping, ambiguity, uncertainty aversion
Heterogeneous Time Preferences and Interest Rates - The Preferred Habitat Theory Revisited
The influence of heterogeneous time preferences on the term structure is investigated. Motivated by the Preferred Habitat Theory of Modigliani and Sutch, a model for intertemporal preferences accounting for preferred habitats is proposed. In a heterogeneous world, preferred habitats can explain humps in the yield curve. Agents with a long habitat prefer long term bonds to shorter instruments as the Preferred Habitat Theory predicts.Term Structure, Heterogeneity, Preferred Habitats
Generic Determinacy of Equilibria with Local Substitution
Consumption of a good at one point in time is a substitute for consumption of the same good an instant earlier or later. Utility functions which conform to this fact must necessarily be non-time separable, as Hindy, Huang, and Kreps show. When agents' utility functions are non-time separable in the required way, the price space consists of semimartingales with an absolutely continuous compensator. In general, this space is not closed under taking pointwise maxima, that is, it is not a lattice. Therefore, neither the Mas-Colell/Richard existence theorem nor the determinacy theorem by Shannon/Zame apply. In a paper with Peter Bank, existence is established for such intertemporal economies; here, I show that generically, the number of equilibria is finite and that equilibrium allocations depend continuously on endowments. The notion of genericity is (finite) prevalence as developed by Anderson/Zame.
Optimal consumption choice with intolerance for declining standard of living
Duesenberry introduced the notion of a ratchet investor who does not tolerate any decline in her consumption rate. We connect the demand behavior of such an agent to the behavior of standard time-additive agents. A ratchet investor demands the running maximum of the optimal plan a conventional time-additive investor with lower initial wealth would choose.intertemporal consumption choice, habit formation, non-time separable utility
Imperfect Information Leads to Complete Markets if Dividends are Diffusions
A pure exchange economy with a financial market is studied where aggregate dividends are modeled as a diffusion. The dynamics of the diffusion are allowed to depend on factors which are unobservable to the agents and have to be estimated. With perfect information, the asset market would be incomplete because there are more factors than traded assets. Imperfect information reduces the number of observable risks, but also the number of admissible portfolio strategies. It is shown that, as long as the observable dividend stream is a diffusion, the asset market is complete. It is therefore possible to establish the existence of an equilibrium with dynamically complete markets that leads to the same allocation as the Arrow-Debreu equilibrium.Complete Markets, General Equilibrium, Imperfect Information, Asset Pricing
The Foster-Hart Measure of Riskiness for General Gambles
Foster and Hart proposed an operational measure of riskiness for discrete
random variables. We show that their defining equation has no solution for many
common continuous distributions including many uniform distributions, e.g. We
show how to extend consistently the definition of riskiness to continuous
random variables. For many continuous random variables, the risk measure is
equal to the worst--case risk measure, i.e. the maximal possible loss incurred
by that gamble. We also extend the Foster--Hart risk measure to dynamic
environments for general distributions and probability spaces, and we show that
the extended measure avoids bankruptcy in infinitely repeated gambles
On Equilibrium Prices in Continuous Time
We combine general equilibrium theory and theorie generale of stochastic
processes to derive structural results about equilibrium state prices
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