Papers by Daniel Hernandez
Scientific Journal of Applied Social and Clinical Science
Communications on Stochastic Analysis
This paper considers mixed strategies for two player, zero sum differential games on a finite tim... more This paper considers mixed strategies for two player, zero sum differential games on a finite time interval. Motivated by the classical result in static games that ensures the existence of a saddle point when mixed strategies are allowed for both players, we extend those ideas to differential games, introducing a Law of Large Numbers game, for which the value function coincides with the limit of discrete time Markov games. Finally, of particular interest is the class of strategies called approximately optimal Markov strategies, which are studied in the last part.
As infecções respiratórias agudas (IRA) são um grupo de doenças complexas e comuns, que são impor... more As infecções respiratórias agudas (IRA) são um grupo de doenças complexas e comuns, que são importantes causas de mortalidade nos países desenvolvidos e em desenvolvimento. Este trabalho tem como objetivo elaborar um Projeto de Intervenção visando a educação da população atendida na ESF Bouganville sobre as causas, complicações e prevenção das Infecções Respiratórias Agudas em crianças de 0-14 anos na área de abrangência da equipe "Bouganville, da Estratégia de Saúde da Família do Município de Sete Lagoas, em Minas Gerais. Foi realizada uma revisão de literatura para subsidiar o planejamento através das seguintes bases de dados: Biblioteca Virtual em Saúde, Biblioteca Virtual da Universidade Federal de Minas Gerais, SciELO e LILACS. Os artigos disponíveis nessas bases de dados, bem como publicações em livros e revistas médicas foram selecionados conforme sua relevância e como critério de inclusão foram aceitas publicações nacionais e manuais do Ministério da Saúde. Elaboramos u...
HAL (Le Centre pour la Communication Scientifique Directe), 2011
ODEON, 2017
En este artículo se hace una presentación del trading de alta frecuencia, junto con sus caracterí... more En este artículo se hace una presentación del trading de alta frecuencia, junto con sus características y estrategias. Posteriormente, bajo el contexto de transacciones de alta frecuencia (HFT), se desarrolla un modelo de creación de mercado, conducido por un agente cuyas posibilidades de negociación en el mercado bursátil se desarrollan a través de órdenes límite y órdenes de mercado; también puede presentar órdenes agresivas con el objetivo de enfrentar los riesgos de inventario, de selección adversa y de ejecución, los cuales son los riesgos a los que el agente se encuentra expuesto.
Mathematical Finance, 2016
We study a robust portfolio optimization problem under model uncertainty for an investor with log... more We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible Lévy triplets, that is, possible instantaneous drift, volatility, and jump characteristics of the price process. We show that an optimal investment strategy exists and compute it in semi‐closed form. Moreover, we provide a saddle point analysis describing a worst‐case model.
SIAM Journal on Control and Optimization, 2016
We revisit a stochastic control problem of optimally modifying the underlying spectrally negative... more We revisit a stochastic control problem of optimally modifying the underlying spectrally negative Lévy process. A strategy must be absolutely continuous with respect to the Lebesgue measure, and the objective is to minimize the total costs of the running and controlling costs. Under the assumption that the running cost function is convex, we show the optimality of a refraction strategy. We also obtain the convergence of the optimal refraction strategies and the value functions, as the control set is enlarged, to those in the relaxed case without the absolutely continuous assumption. Numerical results are further given to confirm these analytical results.
Stochastic Processes and their Applications, 2015
We study a zero-sum game where the evolution of a spectrally one-sided Lévy process is modified b... more We study a zero-sum game where the evolution of a spectrally one-sided Lévy process is modified by a singular controller and is terminated by the stopper. The singular controller minimizes the expected values of running, controlling and terminal costs while the stopper maximizes them. Using fluctuation theory and scale functions, we derive a saddle point and the value function of the game. Numerical examples under phase-type Lévy processes are also given.
Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
This work deals with Markov chains with finite state endowed with a real valued cost function. It... more This work deals with Markov chains with finite state endowed with a real valued cost function. It is assumed that the Markov process has a single recurrent class, but the set of transient states is not necessarily empty. The Varadhan's functional measures the exponential rate of growth of an aggregated cost function. The main goal of this paper is to
The Annals of Applied Probability, 2015
We consider a stochastic differential equation that is controlled by means of an additive finite-... more We consider a stochastic differential equation that is controlled by means of an additive finite-variation process. A singular stochastic controller, who is a minimizer, determines this finite-variation process, while a discretionary stopper, who is a maximizer, chooses a stopping time at which the game terminates. We consider two closely related games that are differentiated by whether the controller or the stopper has a first-move advantage. The games' performance indices involve a running payoff as well as a terminal payoff and penalize control effort expenditure. We derive a set of variational inequalities that can fully characterize the games' value functions as well as yield Markovian optimal strategies. In particular, we derive the explicit solutions to two special cases and we show that, in general, the games' value functions fail to be C 1. The nonuniqueness of the optimal strategy is an interesting feature of the game in which the controller has the first-move advantage.
SPIE Proceedings, 2012
ABSTRACT Scan time of spectral-CTs is much longer than conventional CTs due to limited number of ... more ABSTRACT Scan time of spectral-CTs is much longer than conventional CTs due to limited number of x-ray photons detectable by photon-counting detectors. However, the spectral pixel information in spectral-CT has much richer information on physiological and pathological status of the tissues than the CT-number in conventional CT, which makes the spectral- CT one of the promising future imaging modalities. One simple way to reduce the scan time in spectral-CT imaging is to reduce the number of views in the acquisition of projection data. But, this may result in poorer SNR and strong streak artifacts which can severely compromise the image quality. In this work, spectral-CT projection data were obtained from a lab-built spectral-CT consisting of a single CdTe photon counting detector, a micro-focus x-ray tube and scan mechanics. For the image reconstruction, we used two iterative image reconstruction methods, the simultaneous iterative reconstruction technique (SIRT) and the total variation minimization based on conjugate gradient method (CG-TV), along with the filtered back-projection (FBP) to compare the image quality. From the imaging of the iodine containing phantoms, we have observed that SIRT and CG-TV are superior to the FBP method in terms of SNR and streak artifacts.
Conference on Lasers and Electro-Optics 2012, 2012
ABSTRACT We demonstrate optical trapping and rotation of microparticles and bacteria with propell... more ABSTRACT We demonstrate optical trapping and rotation of microparticles and bacteria with propelling beams. The rotation is achieved in a tweezers-like setting and fully controlled by SLM without mechanical movement or phase-sensitive interference.
Recent Developments in Mathematical Finance - Proceedings of the International Conference on Mathematical Finance, 2001
AbstractThis paper presents an application of risk sensitive control theory in financial decision... more AbstractThis paper presents an application of risk sensitive control theory in financial decision making. A variation of Merton's continuous-time intertemporal capital asset pricing model is investigated where the investor's infinite horizon objective is to maximize the portfolio's risk adjusted growth rate. In earlier studies it was assumed either that the residuals associated with the assets are uncorrelated with the residuals associated with the factors or that there are no exogenous constraints like short selling restrictions. Here we develop computational procedures for the case where both of these assumptions are removed. Our approach is to first approximate the continuous time problem with a discrete time controlled Markov chain. We then solve the latter using the method of successive approximations for risk sensitive Markov decision chains. We show by numerical example that our approach is feasible, at least for cases where there are only a few factors. Our results suggest that when the hedging term is dominated by the myopic term for the corresponding unconstrained problem, then the optimal strategy computed for the constrained problem differs very little from the optimal myopic strategy for the same constrained problem.
2008 American Control Conference, 2008
In this paper the connection between the indifference price and risk sensitive control is explore... more In this paper the connection between the indifference price and risk sensitive control is explored for stochastic volatility models. It is proved that the indifference price of a European option can be written as the difference of the value functions of two different stochastic optimal control problems. The quasilinear PDEs involved in the solution of this problem are written and under suitable conditions a verification theorem is given.
2007 American Control Conference, 2007
We analyze the stochastic control approach to the dynamic maximization of the robust utility of c... more We analyze the stochastic control approach to the dynamic maximization of the robust utility of consumption and investment. The robust utility functionals are defined in terms of logarithmic utility and a dynamically consistent convex risk measure. The underlying market is modeled by a diffusion process whose coefficients are driven by an external stochastic factor process. Our main results give conditions on the minimal penalty function of the robust utility functional under which the value function of our problem can be identified with the unique classical solution of a quasilinear PDE within a class of functions satisfying certain growth conditions.
Theory of Probability & Its Applications, 2008
This work concerns Markov chains with finite state space. Given a real-valued cost function on th... more This work concerns Markov chains with finite state space. Given a real-valued cost function on the state space, the corresponding Varadhan's function, measuring the exponential growth rate of the aggregated costs, is characterized as the unique limit of the fixed points ...
Systems & Control Letters, 1996
In this paper we consider in nite horizon risk-sensitive control of Markov processes with discret... more In this paper we consider in nite horizon risk-sensitive control of Markov processes with discrete time and denumerable state space. This problem is solved proving, under suitable conditions, that there exists a bounded solution to the dynamic programming equation. The dynamic programming equation is transformed into an Isaacs equation for a stochastic game; and the vanishin discount method is used to study its solution. In addtion, we prove that the existence conditions are as well necessary.
Stochastic Processes and their Applications, 2007
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.
Statistics & Risk Modeling, 2006
SUMMARY We give an explicit PDE characterization for the solution of a robust utility maximizatio... more SUMMARY We give an explicit PDE characterization for the solution of a robust utility maximization problem in an incomplete market model, whose volatility, interest rate process, and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in terms of a HARA utility function with negative risk aversion and a dynamically consistent coherent risk measure, which allows for model uncertainty in the distributions of both the asset price dynamics and the factor process. Our method combines two recent advances in the theory of optimal investments: the general duality theory for robust utility maximization and the stochastic control approach to the dual problem of determining optimal martingale measures.
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Papers by Daniel Hernandez