Paola Tardelli

Existence of Optimal Controls for Partially Observed Jump Processes

A partially observable control problem for an Rd-valued jump process with counting observations is studied. The state and the observations may be strongly dependent and, in particular, the two processes may jump together. An equivalent separated problem is introduced and the existence of an optimal control for the separated problem is obtained in the class of relaxed and generalized controls. Equivalence between the initial problem and the relaxed generalized separated control problem is discussed.

Risk-neutral measures and pricing for a pure jump price process: A stochastic control approach

This article considers the asset price movements in a financial market when risky asset prices are modeled by marked point processes. Their dynamics depend on an underlying event arrivals process, modeled again by a marked point process. Taking into account the presence of catastrophic events, the possibility of common jump times between the risky asset price process and the arrivals process is allowed. By setting and solving a suitable control problem, the characterization of the minimal entropy martingale measure is obtained. In a particular case, a pricing problem is also discussed.

An approximation method for controlled discrete jump processes under partial observations

The paper is concerned with control and filtering of a discrete jump Markov process when only the total number of jumps is observed. A partially observable control problem is considered and equivalence between this problem and the separated one is proved. A technique to approximate the value function, under some suitable assumptions, is presented.

Utility maximization in a pure jump model with partial observation

This article considers the asset price movements in a financial market when risky asset prices are modeled by marked point processes. Their dynamics depend on an underlying event arrivals process—a marked point process having common jump times with the risky asset price process. The problem of utility maximization of terminal wealth is dealt with when the underlying event arrivals process is assumed to be unobserved by the market agents using, as the main tool, backward stochastic differential equations. The dual problem is studied. Explicit solutions in a particular case are given.

Probabilistic prediction of credit ratings: a filtering approach

Abstract In a financial market, to analyze the credit quality of firms, this note proposes a dynamical model. The population of firms is divided into a finite number of classes, depending on their credit status. The cardinality of the population can increase during the time, since new firms can enter in the market. Due to changes in credit quality and to the defaults, each firm can move from a class to another, or can go to the class of the defaulted firms. Different rating agencies are considered, each of them defines its own partition of the population. Aim of this note is to find the probabilistic prediction of the actual partition of the population, and of the conditional distribution of the distance to defaults. In a partial observing setting, this topic is discussed using stochastic filtering techniques.