Bubbles in assets with finite life

We study the speculative value of a finitely lived asset when investors disagree and short sales are limited. In this case, investors are willing to pay a speculative value for the resale option they obtain when they acquire the asset. Using martingale arguments, we characterize the equilibrium spec...

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Vydáno v:Mathematics and financial economics Ročník 13; číslo 3; s. 429 - 458
Hlavní autoři: Berestycki, Henri, Bruggeman, Cameron, Monneau, Regis, Scheinkman, José A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019
Springer Nature B.V
Témata:
Applications of Mathematics
Assets
Dynamic programming
Economic models
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Fixed points (mathematics)
Insurance
Investors
Macroeconomics/Monetary Economics//Financial Economics
Management
Martingales
Mathematics
Mathematics and Statistics
Quantitative Finance
Resale
Sales
Statistics for Business
Taxation
Transactions
Viscosity
Willingness to pay
Heterogeneous beliefs
Non-local free boundary problem
Asset-price bubble
Stochastic control
G12
G1
Dynamic programming
G14
Finitely-lived financial asset
G18
ISSN:1862-9679, 1862-9660
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Popis
Shrnutí:We study the speculative value of a finitely lived asset when investors disagree and short sales are limited. In this case, investors are willing to pay a speculative value for the resale option they obtain when they acquire the asset. Using martingale arguments, we characterize the equilibrium speculative value as a solution to a fixed point problem for a monotone operator F . A Dynamic Programming Principle applies and is used to show that the minimal solution to the fixed-point problem is a viscosity solution of a naturally associated (non-local) obstacle problem. Combining the monotonicity of the operator F and a comparison principle for viscosity solutions to the obstacle problem we obtain several comparison of solution results. We also use a characterization of the exercise boundary of the obstacle problem to study the effect of an increase in the costs of transactions on the value of the bubble and on the volume of trade, and in particular to quantify the effect of a small transaction (Tobin) tax.
Bibliografie:ObjectType-Article-1
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ISSN:1862-9679
1862-9660
DOI:10.1007/s11579-018-0233-4