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on Utility Models and Prospect Theory |
| By: | Ikefuji, M.; Laeven, R.J.A.; Magnus, J.R.; Muris, C.H.M. (Tilburg University, Center for Economic Research) |
| Abstract: | This note proposes the Burr utility function. Burr utility is a flexible two-parameter family that behaves approximately power-like (CRRA) remote from the origin, while exhibiting exponential-like (CARA) features near the origin. It thus avoids the extreme behavior of the power family near the origin. We show how to characterize Burr utility as a special case in the general class of utility functions with non-increasing and convex absolute risk aversion, and non-decreasing and concave relative risk aversion. We further show its connection to the Burr probability distribution. A related class of generalized exponential utility functions is also studied. |
| Keywords: | Cardinal scale;Utility function;Harmonic absolute risk aversion (HARA);Exponential utility;Power utility. |
| JEL: | D81 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:201081&r=upt |
| By: | Ramana Nanda (Harvard Business School, Entrepreneurial Management Unit); Matthew Rhodes-Kropf (Harvard Business School, Entrepreneurial Management Unit) |
| Abstract: | Investors in risky startups who stage their investments face financing risk -that is, the risk that later stage investors will not fund the startup, even if the fundamentals of the firm are still sound. We show that financing risk is part of a rational equilibrium where investors can flip from investing to not investing in certain sectors of the economy. We further demonstrate that financing risk has the greatest impact on firms with the most real option value. Hence, the mix of projects funded and type of investors who are active varies with the level of financing risk in the economy. We also highlight that some extremely novel technologies may in fact need `hot' financial markets to get through the initial period of diffusion. Our work underscores that financial markets may play a much larger and under-studied role in creating and magnifying bubbles of innovation in the real economy. |
| Date: | 2010–08 |
| URL: | http://d.repec.org/n?u=RePEc:hbs:wpaper:11-013&r=upt |
| By: | Kocher, Martin G.; Pahlke, Julius; Trautmann, Stefan T. |
| Abstract: | Auctions often involve goods exhibiting a common knowledge ex-post risk that is independent of buyers’ private values or their signals regarding common value components. Esö and White (2004) showed theoretically that ex-post risk leads to precautionary bidding for DARA bidders: Agents reduce their bids by more than their appropriate risk premium. Testing precautionary bidding with data from the field seems almost impossible. We conduct experimental first-price auctions that allow us to directly identify the precautionary premium and find clear evidence for precautionary bidding. Bidders are significantly better off when a risky object rather than an equally valued sure object is auctioned. Our results are robust if we control for potentially confounding decision biases. |
| Keywords: | precautionary bidding; prudence; auction; experiment |
| JEL: | C91 D44 D81 |
| Date: | 2010–08 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:11743&r=upt |
| By: | Ikefuji, M.; Laeven, R.J.A.; Magnus, J.R.; Muris, C.H.M. (Tilburg University, Center for Economic Research) |
| Abstract: | We introduce an accurate, easily implementable, and fast algorithm to compute optimal decisions in discrete-time long-horizon welfaremaximizing problems. The algorithm is useful when interest is only in the decisions up to period T, where T is small. It relies on a flexible parametrization of the relationship between state variables and optimal total time-discounted welfare through scrap value functions. We demonstrate that this relationship depends on the boundedness, half-boundedness, or unboundedness of the utility function, and on whether a state variable increases or decreases welfare. We propose functional forms for this relationship for large classes of utility functions and explain how to identify the parameters. |
| Keywords: | Scrap value function;Dynamic optimization;Computation;Short horizon. |
| JEL: | C61 C63 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:201077&r=upt |
| By: | Seamus Hogan (University of Canterbury); Laura Meriluoto (University of Canterbury) |
| Abstract: | Consider a model in which a consumer faces a lottery with j other people for a prize, so that the probability of winning the prize is 1/(j+1). Now let j be a random variable, determined by the binomial distribution. Specifically, let there be n potential competitors for the consumer in the lottery, each with an independent probability of ? of being a competitor. In this note, we show how the resulting expression for the expected value of 1/(j+1) using binomial probabilities can be simplified by means of the binomial theorem. |
| Keywords: | Binomial Distribution; Binomial Theorem; Lottery |
| JEL: | C10 C16 |
| Date: | 2010–08–11 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/48&r=upt |