Abstract
We demonstrate that the value of a single threshold investment strategy under stochastic dynamics allowing both continuous fluctuations and instantaneous downward jumps has a certainty equivalent representation in terms of the value of this strategy under risk-adjusted deterministic dynamics, and that this risk adjustment can be made either to the discount rate or to the expected infinitesimal growth rate of the underlying. In this way our analysis characterizes a class of optimal timing problems of irreversible investments for which the solution of the stochastic problem coincides with the solutions of certain risk-adjusted deterministic optimal timing problems.
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Alvarez, L.H.R., Rakkolainen, T.A. Investment timing in presence of downside risk: a certainty equivalent characterization. Ann Finance 6, 317–333 (2010). https://doi.org/10.1007/s10436-008-0100-z
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DOI: https://doi.org/10.1007/s10436-008-0100-z
Keywords
- Downside risk
- Certainty equivalence
- Exponential Lévy process
- Optimal stopping
- Risk adjustment
- Threshold policy