Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals.
Optimal portfolios in Lévy markets under state-dependent bounded utility functions.
Optimal selection of the maximum of a discountable sequence of independent random variables
Optimal sequential multiple hypothesis testing in presence of control variables
Suppose that at any stage of a statistical experiment a control variable that affects the distribution of the observed data at this stage can be used. The distribution of depends on some unknown parameter , and we consider the problem of testing multiple hypotheses , , allowing the data to be controlled by , in the following sequential context. The experiment starts with assigning a value to the control variable and observing as a response. After some analysis, another value for...
Optimal sequential multiple hypothesis tests
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized.
Optimal sequential procedures with Bayes decision rules
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect...
Optimal solutions to stochastic differential inclusions
A martingale problem approach is used first to analyze compactness and continuous dependence of the solution set to stochastic differential inclusions of Ito type with convex integrands on the initial distributions. Next the problem of existence of optimal weak solutions to such inclusions and their dependence on the initial distributions is investigated.
Optimal state estimation of a Markov process from point process observations
Optimal stopping and impulsive control of one-dimensional diffusion processes
Optimal stopping for Markov Processes
In questa nota presentiamo dei nuovi risultati sul problema di tempo d’arresto ottimale per processi di Markov con tempo discreto.
Optimal stopping of a 2-vector risk process
The following problem in risk theory is considered. An insurance company, endowed with an initial capital a > 0, receives insurance premiums and pays out successive claims from two kind of risks. The losses occur according to a marked point process. At any time the company may broaden or narrow down the offer, which entails the change of the parameters of the underlying risk process. These changes concern the rate of income, the intensity of the renewal process and the distribution of claims....
Optimal stopping of a random length sequence of maxima over a random barrier
Optimal stopping of a risk process
Optimal stopping time problems for a risk process where the number N(t) of losses up to time t is a general renewal process and the sequence of ’s represents successive losses are studied. N(t) and ’s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].
Optimal stopping of a sequence of maxima between random and fixed barriers
Optimal stopping of a sequence of maxima over an unobservable sequence of maxima
Optimal stopping with advanced information flow: selected examples
We study optimal stopping problems for some functionals of Brownian motion in the case when the decision whether or not to stop before (or at) time t is allowed to be based on the δ-advanced information , where is the σ-algebra generated by Brownian motion up to time s, s ≥ -δ, δ > 0 being a fixed constant. Our approach involves the forward integral and the Malliavin calculus for Brownian motion.
Optimal transmission of Gaussian signals through a feedback channel.
Optimal transportation for multifractal random measures and applications
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metrics, the volume forms of which coincide with the multifractal random measures.
Optimality of replication in the CRR model with transaction costs
Recently, there has been a growing interest in optimization problems associated with the arbitrage pricing of derivative securities in imperfect markets (in particular, in models with transaction costs). In this paper, we examine the valuation and hedging of European claims in the multiplicative binomial model proposed by Cox, Ross and Rubinstein [5] (the CRR model), in the presence of proportional transaction costs. We focus on the optimality of replication; in particular, we provide sufficient...
Optimisation in space of measures and optimal design
The paper develops an approach to optimal design problems based on application of abstract optimisation principles in the space of measures. Various design criteria and constraints, such as bounded density, fixed barycentre, fixed variance, etc. are treated in a unified manner providing a universal variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. Incorporating the optimal design problems into conventional optimisation framework makes...