Giovanni B. Di Masi

Towards a General Theory of Bond Markets

Abstract.The main purpose of the paper is to provide a mathematical background 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 trading 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.

INFINITE HORIZON RISK SENSITIVE CONTROL OF DISCRETE TIME MARKOV PROCESSES UNDER MINORIZATION PROPERTY

Risk sensitive control of Markov processes satisfying the minorization property is studied using splitting techniques. Existence of solutions to the multiplicative Poisson equation is shown. Approximation by uniformly ergodic controlled Markov processes is introduced, which allows us to show the existence of solutions to the infinite horizon risk sensitive Bellman equation.

On measure transformations for combined filtering and parameter estimation in discrete time

Combined filtering and parameter estimation in discrete time is studied as a nonlinear filtering problem. The measure transformation approach is used and the Zakai equation derived. Some applications are discussed.

An approach to discrete-time stochastic control problems under partial observation

We consider a general class of discrete-time nonlinear stochastic control problems with partial observation, for which in general only

Remarks on Risk Neutral and Risk Sensitive Portfolio Optimization

\varepsilon

Non-linear filtering with discontinuous observations and applications to life sciences

-optimal controls exist, and provide a method for explicitly computing them. Transforming, as usual, these problems into equivalent ones with complete observation leads to various difficulties, in particular to a nonlinear filtering problem. We first define a subclass of the given problems such that the associated nonlinear filtering problem can be explicitly solved and, for each

An Adaptive Linear Approach to Nonlinear Filtering

\delta > 0

Adaptive methods for piecewise linear filtering

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Adaptive control of a partially observable stochastic system

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Portfolio Optimization in Discontinuous Markets under Incomplete Information

-optimal control computed. We then show that, under suitable assumptions, for each original problem and each given