Heath-Jarrow-Morton-Musiela equation with linear volatility
Michal Barski, Jerzy Zabczyk
TL;DR
This paper investigates the existence of solutions to the Heath-Jarrow-Morton-Musiela equation with linear volatility, emphasizing the importance of logarithmic growth conditions of the Laplace exponent.
Contribution
It provides necessary and sufficient conditions for the existence of weak and strong solutions to the equation, advancing theoretical understanding.
Findings
Necessary and sufficient conditions for solution existence
Logarithmic growth conditions of the Laplace exponent are crucial
Clarifies solution criteria for the HJM-Musiela equation with linear volatility
Abstract
The paper is concerned with the problem of existence of solutions for the Heath-Jarrow-Morton equation with linear volatility. Necessary conditions and sufficient conditions for the existence of weak solutions and strong solutions are provided. It is shown that the key role is played by the logarithmic growth conditions of the Laplace exponent.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · advanced mathematical theories · Stochastic processes and financial applications