## Continuous-time asset pricing with ambiguity aversion

### Porchia, Paolo ; Trojani, Fabio (Dir.)

### Thèse de doctorat : Università della Svizzera italiana, 2005 ; 2005ECO005.

This Thesis is structured in two Chapters, each aimed at contributing to the existing literature by exploring the effects of ambiguity aversion on two classical equilibrium asset pricing problems: the term structure of interest rates and two-agents equilibrium. In both cases, ambiguity aversion is modeled by means of a Max-Min expected utility representation that falls within the Recursive... Plus

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- This Thesis is structured in two Chapters, each aimed at contributing to the existing literature by exploring the effects of ambiguity aversion on two classical equilibrium asset pricing problems: the term structure of interest rates and two-agents equilibrium. In both cases, ambiguity aversion is modeled by means of a Max-Min expected utility representation that falls within the Recursive Multiple Priors class - thereby delivering dynamic consistency of the optimal policies of the agents. The set of likelihood used in the preference orderings representation is identified by means of a bound on the maximum 'distance' between admissible probability measures and a reference one, interpreted as approximate description of the true data generating model. The first Chapter of the Thesis, 'A General Treatment of Equilibrium under Ambiguity' considers a continuous-time pure exchange economy populated by two agents, whose decisions rely on a whole set of possible contaminations of a reference probabilistic model. Given that they adopt a form of max-min expected utility representation, agents select the worst-case model among those considered as relevant. The methodology applied in order to characterize equilibrium equity premia and stock returns volatility is based on a weak notion of aggregation of the single agents into a representative agent, whose preferences depend on an additional state variable acting as a proxy for the stochastic shifts of the cross-sectional wealth distribution due to the different beliefs selected in equilibrium by agents. Closed form solutions for key equilibrium quantities are detailed for markovian specifications of the stochastic opportunity set. This modelling framework suggests a possible explanation of the equity premium puzzle; what is more, endogenous cycles of restricted stock market participation are obtained, without imposing exogenous policy restrictions on agents. The second Chapter, 'Ambiguity aversion, bond pricing, and the non robustness of some affine term structures', develops a continuous time general equilibrium model of the term structure of interest rates where economic agents are averse to model uncertainty and consider the possibility of a misspecified dynamic model for the latent random factors driving interest rates. A small concern for ambiguity significantly affects the implied term structures in equilibrium and drives the prices of common derivative securities toward the patterns observed in fixed income markets. Indeed, equilibrium risk premia and interest rates have a different functional form than in the standard model, due to an ambiguity aversion premium. Moreover, otherwise unpriced factors in the standard model receive a premium for model uncertainty which is of a particularly rich structure in the multiple factors setting. Examples of the impact of ambiguity aversion on popular factor models of the term structure are derived, both in cases for which the `level of concern' ambiguity is time- varying and in cases for which it is time invariant.