Oblique derivative problems and invariant measures
On a class of discrete generation interacting particle systems.
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 a role of predictor in the filtering stability.
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 almost sure convergence of modified Euler-Peano approximation of solution to an S.D.E. driven by a semimartingale
On an optimum principle for partially observed controlled jump Markovian processes
On approximations of nonzero-sum uniformly continuous ergodic stochastic games
We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].
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 Definiteness Of Certain Matrix Functions Of A Matrix
On European option pricing under partial information
We consider a European option pricing problem under a partial information market, i.e., only the security's price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering...
On exact null controllability of Black-Scholes equation
In this paper we discuss the exact null controllability of linear as well as nonlinear Black–Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with ...
On exponentially discounted adaptive control
On filtering over Îto-Volterra observations.
On improving sensitivity of the Kalman filter
The impact of additive outliers on a performance of the Kalman filter is discussed and less outlier-sensitive modification of the Kalman filter is proposed. The improved filter is then used to obtain an improved smoothing algorithm and an improved state-space model parameters estimation.