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Continuous Markov equilibria with quasi-geometric discounting
We prove that the standard quasi-geometric discounting model used in dynamic consumer theory and political economics does not possess continuous Markov perfect equilibria (MPE) if there is a strictly positive lower bound on wealth. We also show that, at points of discontinuity, the decision maker strictly prefers lotteries over the next period's assets. We then extend the standard model to have lotteries and establish the existence of an MPE with continuous decision rules. The models with and without lotteries are numerically compared, and it is shown that the model with lotteries behaves ...
Lottery Loans in the Eighteenth Century
In the 18th century Britain frequently issued lottery loans, selling bonds whose size was determined by a draw soon after the sale. The probability distribution was perfectly known ex-ante and highly skewed. After the draw the bonds were identical (except for size) and indistinguishable from regular bonds. I collect market prices for the lottery tickets and show that investors were paying a substantial premium to be exposed to this purely artificial risk. I show that investors were well-to-do and included many merchants and bankers. I turn to cumulative prospect theory to make sense of these ...