Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

DOI10.1080/14697680802595692zbMath1185.91179arXivmath/0702622OpenAlexW2153726546MaRDI QIDQ5189713

Carlo Marinelli

Publication date: 11 March 2010

Published in: Quantitative Finance (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702622

zbMATH Keywords

differential equationsterm structurecontrol of stochastic systemscontinuous time financeAmerican style derivative securities

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Derivative securities (option pricing, hedging, etc.) (91G20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (3)

Mean reversion for HJMM forward rate models ⋮ On a stochastic heat equation with first order fractional noises and applications to finance ⋮ Stochastic evolution equations in Banach spaces and applications to the Heath-Jarrow-Morton-Musiela equations

Cites Work

• A theory of bond portfolios
• Exponential moments for HJM models with jumps
• Towards a general theory of bond markets
• Harnack and functional inequalities for generalized Mehler semigroups.
• Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift
• Lévy term structure models: no-arbitrage and completeness
• Generalized Mehler semigroups: The non-Gaussian case
• Invariant measures for the Musiela equation with deterministic diffusion term
• A model of the term structure of interest rates based on Lévy fields
• A note of invariant measures for HJM models
• Credit risk with infinite dimensional Lévy processes
• Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation
• GENERATORS OF MEHLER-TYPE SEMIGROUPS AS PSEUDO-DIFFERENTIAL OPERATORS
• Ergodicity for Infinite Dimensional Systems

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