Oblique derivative problems and invariant measures
On a class of forward-backward stochastic differential systems in infinite dimensions.
On a non-linear semi-group associated with stochastic optimal control and its excessive majorant
On adaptive control of a partially observed Markov chain
A control problem for a partially observable Markov chain depending on a parameter with long run average cost is studied. Using uniform ergodicity arguments it is shown that, for values of the parameter varying in a compact set, it is possible to consider only a finite number of nearly optimal controls based on the values of actually computable approximate filters. This leads to an algorithm that guarantees nearly selfoptimizing properties without identifiability conditions. The algorithm is based...
On adaptive control of Markov chains using nonparametric estimation
Two adaptive procedures for controlled Markov chains which are based on a nonparametric window estimation are shown.
On adaptive control of Markov processes
On additive and multiplicative (controlled) Poisson equations
Assuming that a Markov process satisfies the minorization property, existence and properties of the solutions to the additive and multiplicative Poisson equations are studied using splitting techniques. The problem is then extended to the study of risk sensitive and risk neutral control problems and corresponding Bellman equations.
On an optimum principle for partially observed controlled jump Markovian processes
On Bellman systems without zero order term in the context of risk sensitive differential games
Bellman systems corresponding to stochastic differential games arising from a cost functional which models risk aspects are considered. Here it leads to diagonal elliptic systems without zero order term so that no simple -estimate is available.
On controlled Markov processes with average cost criterion
On impulsive control with long run average cost criterion
On nearly selfoptimizing strategies for multiarmed bandit problems with controlled arms
Two kinds of strategies for a multiarmed Markov bandit problem with controlled arms are considered: a strategy with forcing and a strategy with randomization. The choice of arm and control function in both cases is based on the current value of the average cost per unit time functional. Some simulation results are also presented.
On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance
We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum...
On one method of analysis of linear systems with random stationary coefficients
On optimal stopping of inhomogeneous standard Markov processes.
On option pricing in the multidimensional Cox-Ross-Rubinstein model
Option pricing in the multidimensional case, i.e. when the contingent claim paid at maturity depends on a number of risky assets, is considered. It is assumed that the prices of the risky assets are in discrete time subject to binomial disturbances. Two approaches to option pricing are studied: geometric and analytic. A numerical example is also given.
On risk sensitive control of regular step Markov processes
Risk-sensitive control problem of regular step Markov processes is considered, firstly when the control parameters are changed at shift times and then in the general case.
On self-optimizing control of Markov processes
On some recent aspects of stochastic control and their applications.
On steady state minimum variance control strategy