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Decomposition of large-scale stochastic optimal control problems

Kengy Barty, Pierre Carpentier, Pierre Girardeau (2010)

RAIRO - Operations Research

In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework...

Degenerate Eikonal equations with discontinuous refraction index

Pierpaolo Soravia (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We study the Dirichlet boundary value problem for eikonal type equations of ray light propagation in an inhomogeneous medium with discontinuous refraction index. We prove a comparison principle that allows us to obtain existence and uniqueness of a continuous viscosity solution when the Lie algebra generated by the coefficients satisfies a Hörmander type condition. We require the refraction index to be piecewise continuous across Lipschitz hypersurfaces. The results characterize the value...

Deterministic minimax impulse control in finite horizon: the viscosity solution approach

Brahim El Asri (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We study here the impulse control minimax problem. We allow the cost functionals and dynamics to be unbounded and hence the value functions can possibly be unbounded. We prove that the value function of the problem is continuous. Moreover, the value function is characterized as the unique viscosity solution of an Isaacs quasi-variational inequality. This problem is in relation with an application in mathematical finance.

Discrete time risk sensitive portfolio optimization with consumption and proportional transaction costs

Łukasz Stettner (2005)

Applicationes Mathematicae

Risk sensitive and risk neutral long run portfolio problems with consumption and proportional transaction costs are studied. Existence of solutions to suitable Bellman equations is shown. The asymptotics of the risk sensitive cost when the risk factor converges to 0 is then considered. It turns out that optimal strategies are stationary functions of the portfolio (portions of the wealth invested in assets) and of economic factors. Furthermore an optimal portfolio strategy for a risk neutral control...

Discrete-time Markov control processes with recursive discount rates

Yofre H. García, Juan González-Hernández (2016)

Kybernetika

This work analyzes a discrete-time Markov Control Model (MCM) on Borel spaces when the performance index is the expected total discounted cost. This criterion admits unbounded costs. It is assumed that the discount rate in any period is obtained by using recursive functions and a known initial discount rate. The classic dynamic programming method for finite-horizon case is verified. Under slight conditions, the existence of deterministic non-stationary optimal policies for infinite-horizon case...

Dynamic portfolio optimization with risk management and strategy constraints

Csilla Krommerová, Igor Melicherčík (2014)

Kybernetika

We investigate the problem of power utility maximization considering risk management and strategy constraints. The aim of this paper is to obtain admissible dynamic portfolio strategies. In case the floor is guaranteed with probability one, we provide two admissible solutions, the option based portfolio insurance in the constrained model, and the alternative method and show that none of the solutions dominate the other. In case the floor is guaranteed partially, we provide one admissible solution,...

Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching

Paul Gassiat, Fausto Gozzi, Huyên Pham (2015)

Banach Center Publications

We consider an illiquid financial market with different regimes modeled by a continuous time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the market regime. Moreover, the risky asset price is subject to liquidity shocks, which change its rate of return and volatility, and induce jumps on its dynamics. In this setting, we study the problem of an economic agent optimizing her expected utility from consumption...

Dynamic Programming for the stochastic Navier-Stokes equations

Giuseppe da Prato, Arnaud Debussche (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We solve an optimal cost problem for a stochastic Navier-Stokes equation in space dimension 2 by proving existence and uniqueness of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation.

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