On the Positivity of Local Mild Solutions to Stochastic Evolution Equations
On the Positivity of Local Mild Solutions to Stochastic Evolution Equations
We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is positive if the initial datum is positive. As an application, we discuss the positivity of forward rates in the Heath-Jarrow-Morton model via Musiela's stochastic PDE.
10 pages, no figures
- University of Vienna Austria
- University of Vienna
- University College London United Kingdom
- Polytechnic University of Milan Italy
- UNIVERSITY COLLEGE LONDON, Bartlett School of Planning United Kingdom
Mild solutions, Probability (math.PR), Positivity, Mathematical Finance (q-fin.MF), FOS: Economics and business, Mathematics - Analysis of PDEs, HJM model, Quantitative Finance - Mathematical Finance, FOS: Mathematics, Stochastic evolution equations, Mathematics - Probability, Analysis of PDEs (math.AP)
Mild solutions, Probability (math.PR), Positivity, Mathematical Finance (q-fin.MF), FOS: Economics and business, Mathematics - Analysis of PDEs, HJM model, Quantitative Finance - Mathematical Finance, FOS: Mathematics, Stochastic evolution equations, Mathematics - Probability, Analysis of PDEs (math.AP)
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