Stephen LeRoy, UCSB Economics

"Compactifying the Payoff Space: Applications in Financial Economics."

Finance models with a finite number of states and dates have a number of properties that may or may not extend to their infinite counterparts. Whether they do depends how equilibrium is defined. Under sequential equilibrium many properties do not extend to infinite settings. We propose an alternative equilibrium concept that is closer to classical finite Walrasian equilibrium. This involves appending a date called \uffff~H~^ to the finite dates and defining a topology such that the payoff index set so expanded is compact. Payoffs of infinite portfolio strategies are defined as limits of payoffs of finite portfolio strategies. This setup allows a simplified mathematical treatment of a number of topics that are unwieldy when modeled in a setting where the payoff index set is not compact. Topics discussed include Ponzi schemes, payoff bubbles and the doubling strategy.