Multi-period mean-variance portfolio optimization with markov switching parameters

In this paper we deal with a multi-period mean-variance portfolio selection problem with the market parameters subject to Markov random regime switching. We analytically derive an optimal control policy for this mean-variance formulation in a closed form. Such a policy is obtained from a set of interconnected Riccati difference equations. Additionally, an explicit expression for the efficient frontier corresponding to this control law is identified and numerical examples are presented.Investiga-se um modelo multi-dimensional de seleção de carteiras em média-variância, no qual os parâmetros de mercado estão sujeitos a saltos Markovianos. Deriva-se analiticamente uma estratégia de controle ótima em forma fechada para esta formulação de média-variância. Esta estratégia é obtida através de um conjunto de equações a diferenças de Riccati. Adicionalmente, uma expressão explícita para a fronteira eficiente correspondente a este controle ótimo é identificada e exemplos numéricos são apresentados.(CNPq) Brazilian National Research Council(FAPESP) São Paulo Research Foundatio

Fault Detection Filter for Discrete-Time Markov Jump Lur’e Systems

We present the design of H_inf Fault Detection Filter (FDF) for Discrete-time Markov Jump Lur'e Systems with bounded sector condition based on the use of Linear Matrix Inequality (LMI). A numerical example is presented to illustrate the effectiveness of the proposed approach

Arbitrage-Free Conditions and Hedging Strategies for Markets with Penalty Costs on Short Positions

We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficient conditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate a contingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedure for obtaining perfect hedging strategies.CNPq (Brazilian National Research Council) [301067/09-0]Brazilian National Research Council (CNPq)USPUS

Fault Compensation Controller for Markovian Jump Linear Systems

In this paper, we tackle the fault-compensation controller in the context of Marko- vian Jump Linear Systems (MJLS). More specifically, we propose the design of H∞ Fault- Compensation Controllers under the MJLS formulation, which is provided in terms of linear matrices inequalities optimization problems. These particular controllers have as the main motivation the network communication loss which is inherent to any automation process. We present a numerical example of a coupled tank system, where a Monte Carlo simulation illustrates the feasibility of the proposed solution. The results show that the proposed approach is indeed a valuable alternative to compensate for the fault occurrence

Gain-Scheduled Controller for Fault Accommodation in Linear Parameter Varying Systems with Imprecise Measurements

We present the design of H∞ and H2 gain-scheduled fault-accommodation controllers for discrete-time Linear Parameter Varying systems. We design our conditions as Bilinear Matrix Inequalities, assuming that the scheduled parameters are imprecise, which is a commonly found characteristic of practical applications that happens due to measurement noise and inaccuracy on its estimation/acquisition procedure. The proposed solution is based on the use of a multi-simplex approach for solving the main conditions, which guarantees the stability of the system under imprecise measurements on the scheduling parameters. The efficacy of the proposed approach is illustrated with a numerical example

Approximations for optimal stopping and impulsive control of piecewise-deterministic processes

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Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model

Hamilton-Jacobi-Bellman inequality for the average control of piecewise deterministic Markov processes

International audienceThe main goal of this paper is to study the infinite-horizon long run average continuous-time optimal control problem of piecewise deterministic Markov processes (PDMPs) with the control acting continuously on the jump intensity λ and on the transition measure Q of the process. We provide conditions for the existence of a solution to an integro-differential optimality inequality, the so called Hamilton-Jacobi-Bellman (HJB) equation, and for the existence of a deterministic stationary optimal policy. These results are obtained by using the so-called vanishing discount approach, under some continuity and compactness assumptions on the parameters of the problem, as well as some non-explosive conditions for the process