# Invariant measures for the Musiela equation with deterministic diffusion term

## Author

Listed:
• Tiziano Vargiolu

() (Dipartimento di Matematica Pura ed Applicata, UniversitÂ di Padova, via Belzoni 7, I-35131 Padova, Italy Manuscript)

## Abstract

In this article the forward rates equation of the Musiela model is analysed. The equation is studied in the Sobolev spaces $H^1_\gamma({\Bbb R}^+)$ and $H^1({\Bbb R}^+)$. Explicit mild solutions and equivalent conditions for the existence and uniqueness of invariant measures are presented.

## Suggested Citation

• Tiziano Vargiolu, 1999. "Invariant measures for the Musiela equation with deterministic diffusion term," Finance and Stochastics, Springer, vol. 3(4), pages 483-492.
• Handle: RePEc:spr:finsto:v:3:y:1999:i:4:p:483-492
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## Citations

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Cited by:

1. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
2. Zdzislaw Brzezniak & Tayfun Kok, 2016. "Stochastic Evolution Equations in Banach Spaces and Applications to Heath-Jarrow-Morton-Musiela Equation," Papers 1608.05814, arXiv.org.
3. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.
4. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

### Keywords

term structure of interest rates; stochastic partial differential equations; mild solutions; invariant measures; $C^0$-semigroups in Hilbert spaces;

### JEL classification:

• E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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