Optimal Changes of Gaussian Measures, with Application to Finance

Henry Schellhorn ()
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Henry Schellhorn: HEC, University of Lausanne and FAME

FAME Research Paper Series from International Center for Financial Asset Management and Engineering

Abstract: We derive optimality conditions and calculate approximate solutions to the problem of determining the optimal speed of mean reversion to be applied to a Gaussian state variable. The optimality criterion is the minimization of the variance of the Radon-Nikodym derivative of the measure ”with mean-reversion ” with respect to the measure ”without mean-reversion ”under constraints. Our results have two main applications. First, we show that we can increase the speed of performing resimulation and sensitivity analysis in a Monte Carlo simulation. Second, we show that there is some phase delay between the optimal speed of mean-reversion and volatility. Incorporating this effect into preference modelling could contribute to solve the equity premium puzzle in finance.

Keywords: Equity premium puzzle; Monte Carlo simulation; change of measure (search for similar items in EconPapers)
JEL-codes: C65 G12 (search for similar items in EconPapers)
Date: 2002-05
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Persistent link: https://EconPapers.repec.org/RePEc:fam:rpseri:rp127

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