Towards a general theory of bond markets
TLDR
It is shown that a market is approximately complete iff an equivalent martingale measure is unique and two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions are suggested.Abstract:
To the memory of our friend and colleague Oliviero Lessi. Abstract. The main purpose of the paper is to provide a mathematical back- ground for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding to a trad- ing strategy which is a measure-valued predictable process. The existence of an equivalent martingale measure is discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show that a market is approximately complete iff an equivalent martingale measure is unique.read more
Citations
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References
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A Theory of the Term Structure of Interest Rates.
TL;DR: In this paper, the authors use an intertemporal general equilibrium asset pricing model to study the term structure of interest rates and find that anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices.
Journal ArticleDOI
An equilibrium characterization of the term structure
TL;DR: In this article, the authors derived a general form of the term structure of interest rates and showed that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation.
Book
Limit Theorems for Stochastic Processes
Jean Jacod,Albert N. Shiryaev +1 more
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
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Stochastic integration and differential equations
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.
Book
Stochastic Equations in Infinite Dimensions
Giuseppe Da Prato,Jerzy Zabczyk +1 more
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.