Applications of Eigenfunction Expansions in Continuous-Time Finance
AbstractWe provide exact solutions for two closely related valuation problems in continuous-time finance. The first problem is to value generalized European-style options on stocks that pay dividends at a constant dollar rate. The second problem is to find the yield curve associated with the economy of R. C. Merton's "An Asymptotic Theory of Growth Under Uncertainty." In Merton's economic growth model, the interest rate process has a volatility linear in the rate level and a linear/quadratic drift. Both problems are solved by an eigenfunction expansion technique. The main technical difficulty is handling the problem of payoff functions that are not square-integrable with respect to the natural weight function of the models. Copyright Blackwell Publishers Inc 1998.
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Mathematical Finance.
Volume (Year): 8 (1998)
Issue (Month): 4 ()
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627
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- Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2009. "Spectral decomposition of optimal asset-liability management," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 710-724, March.
- Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
- Lim, Dongjae & Li, Lingfei & Linetsky, Vadim, 2012. "Evaluating callable and putable bonds: An eigenfunction expansion approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1888-1908.
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