160,555 research outputs found
A Bayesian adaptive control approach to risk management in a binomial model
No full textWe consider the problem of shortfall risk minimization when there is uncertainty about the exact stochastic dynamics of the underlying. Starting from the general discrete time model and the approach described in Runggaldier and Zaccaria (1999), we derive explicit analytic solutions for the particular case of a binomial model when there is uncertainty about the probability of an "up-movement". The solution turns out to be a rather intuitive extension of that for the classical Cox-Ross-Rubinstein model
Financial Mathematics: Theory and Problems for Multi-period Models
No full textWith the Bologna Accords a bachelor-master-doctor curriculum has been introduced in various countries with the intention that students may enter the job market already at the bachelor level. Since financial Institutions provide non negligible job opportunities also for mathematicians, and scientists in general, it appeared to be appropriate to have a financial mathematics course already at the bachelor level in mathematics. Most mathematical techniques in use in financial mathematics are related to continuous time models and require thus notions from stochastic analysis that bachelor students do in general not possess. Basic notions and methodologies in use in financial mathematics can however be transmitted to students also without the technicalities from stochastic analysis by using discrete time (multi-period) models for which general notions from Probability suffice and these are generally familiar to students not only from science courses, but also from economics with quantitative curricula.
There do not exists many textbooks for multi-period models and the present volume is intended to fill in this gap. It deals with the basic topics in financial mathematics and, for each topic, there is a theoretical section and a problem section. The latter includes a great variety of possible problems with complete solution
Finanza matematica: teoria e problemi per modelli multiperiodali
No full textLa finanza matematica ha visto un notevole sviluppo in tempi recenti, soprattutto per l'introduzione di strumenti finanziari atti a contenere il rischio nelle operazioni di mercato. Lo studio delle problematiche legate a tali strumenti richiede tecniche matematiche talvolta sofisticate e la maggior parte di queste tecniche sono legate alla teoria della Probabilità.
Gli ambienti finanziari sono quindi divenuti uno sbocco professionale non solo per gli economisti, ma anche per i matematici ed in generale per i laureati delle discipline tecnico-scientifiche. Il presente libro è inteso come testo e nasce dall'esperienza d’insegnamento degli autori. Non esistono molti testi simili a livello internazionale ed il libro intende colmare tale lacuna. Benché concepito maggiormente per un corso di laurea triennale in matematica, esso dovrebbe adattarsi bene anche a corsi di tipo quantitativo per le facoltà di economia
On Necessary Conditions For the Existence of Finite-dimensional Filters In Discrete-time
No full textA Robustness Result for Stochastic Control
No full textThe solution of a stochastic control problem depends on the underlying model, i.e., on the probability measure induced by the model. The real world model may not be known precisely, and so one solves the problem for a hypothetical model that induces a measure generally different but close to the real one.
We investigate two ways to derive a bound on the suboptimality of the hypothetical optimal control when it is used in the real problem. Both bounds are in terms of the Radon-Nikodym derivative of the real world measure with respect to the hypothetical one
On logarithmic transformations in discrete-time stochastic control
No full text"October 1985."Bibliography: p. 20-21.W.J. Runggaldier
Estimates for perturbations of average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains
No full textsummary:This paper deals with Markov decision processes (MDPs) with real state space for which its minimum is attained, and that are upper bounded by (uncontrolled) stochastically ordered (SO) Markov chains. We consider MDPs with (possibly) unbounded costs, and to evaluate the quality of each policy, we use the objective function known as the average cost. For this objective function we consider two Markov control models and . and have the same components except for the transition laws. The transition of is taken as unknown, and the transition of , as a known approximation of . Under certain irreducibility, recurrence and ergodic conditions imposed on the bounding SO Markov chain (these conditions give the rate of convergence of the transition probability in -steps, to the invariant measure), the difference between the optimal cost to drive and the cost obtained to drive using the optimal policy of is estimated. That difference is defined as the index of perturbations, and in this work upper bounds of it are provided. An example to illustrate the theory developed here is added
Pathwise optimality for benchmark tracking
No full textWe consider the problem of investing in a portfolio in order to track or "beat" a given benchmark. We study this problem from the point of view of almost sure/pathwise optimality. We first obtain a control that is optimal in the mean and this control is then shown to be also pathwise optimal. The standard Merton model leads to lognormality of the value process so that it does not possess the required ergodic properties. We obtain ergodicity by transforming the process so that it remains bounded thereby using a method that can be related to a random time change. We furthermore describe a general approach to solve the Hamilton-Jacobi-Bellman equation corresponding to the given problem setup
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