# Ernst L. PresmanRussian Academy of Sciences | RAS · Central Economics and Mathematics Institute

Ernst L. Presman

Doctor of Sciences (Physics and Mathematics)

## About

71

Publications

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880

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## Publications

Publications (71)

An optimal stopping problem of a Markov process with infinite horizon is considered. For the case of discrete time and finite number m of states Sonin proposed an algorithm which allows to find the value function and the stopping set in no more than 2(m-1) steps. The algorithm is based on a modification of a Markov chain on each step, related to th...

A problem of optimal stopping for one-dimensional time-homogeneous regular diffusion with the infinite horizon is considered. The diffusion takes values in a finite or infinite interval ]a,b[. The points a and b may be either natural or absorbing or reflecting. The diffusion may have a partial reflection at a finite number of points. A discounting...

We consider a problem of optimal stopping for geometric Brownian motion Z t on ]0, ∞[ with parameters b, σ and killing intensity r. at the point x there is a partial reflection, so that P x [Z t > x] → (1 + α)/2 as t → 0, −1 < α < 1. The payoff function ¯ g(z) = (z − K) +. The value function is V (z) = sup τ E z ¯ g(Z τ), where supremum is taken ov...

We consider a problem of optimal production control of a single unreliable machine. The objective is to minimize a discounted convex inventory/backlog cost over an infinite horizon. Using the variational analysis methodology, we develop the necessary conditions of optimality in terms of the co-state dynamics. We show that an inventory-threshold con...

An optimal stopping problem of Markov chain with infinite horizon is considered. For the case of finite number m of states, Sonin proposed an algorithm, which allows to find the value function and the stopping set in not more than steps. The algorithm is based on a modification of Markov chain on each step, related with the elimination of the state...

This paper has two main goals: first, to describe a new class of optimal stopping (OS) problems for which the solutions can be found either in an explicit form, or in a finite number of steps, and second, to demonstrate the potential of the state elimination algorithm developed by one of the authors earlier, for the problem of OS of a finite or cou...

The Kolmogorov-Prokhorov theorem is studied on the existence of expectations of random sums by considering a sequence of independent random variables. An integer nonnegative random variable independent of the future with respect to a sequence of independent random variables is also independent of the σ-algebra. The class of nonnegative convex funct...

A Burkholder-type inequality for supermartingales and martingales is proved. The proof reduces to a refinement of the corresponding arguments by S. V. Nagaev, who obtained the inequality with a greater value of the upper bound.

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upp...

This paper is concerned with the problem of production planning in a stochastic manufacturing system with serial machines that are subject to breakdown and repair. The machine capacities are modeled as Markov chains. Since the number of parts in the internal buffers between any two the problem is inherently a state constrained problem. The objectiv...

This paper is concerned with a production planning problem in a two-machine flowshop subject to breakdown and repair of machines subject to nonnegativity constraints on work-in-process. The objective is to choose machine production rates over time to meet the demand facing the flowshop at a minimum long-run average cost. It si shown that the dynami...

We develop a new, unified approach to treating continuous-time stochastic inventory problems with both the average and discounted cost criteria. The approach involves the development of an adjusted discounted cycle cost formula, which has an appealing intuitive interpretation. We show for the first time that an (s, S) policy is optimal in the case...

This work concerns asymptotic study of the joint distribution of the maximum of a sequence of sums and the sums themselves on finite regular Markov chains. To this end, a series of lemmas are demonstrated on factorization of elements of general algebraic rings, as well as factorization identities having interest in themselves which provide a connec...

We consider the problem which informally can be described as follows. Initially a finite set of independent trials is available. If a Decision Maker (DM) chooses to test a specific trial she receives a reward, and with some probability, the process of testing is terminated or the tested trial becomes unavailable but some random finite set (possibly...

We consider the following “silent duel” of m players with a possible economic interpretation. Each player has one “bullet”, which she can shoot at any time during the time interval [0,1]. The probability that the i-th player hits the “target” at moment t is given by an increasing accuracy function f
i
(t). The winner is the player who hits the targ...

We show that the optimal feedback control û in the standard nonhomogeneous LQG-problem with infinite horizon has the following property. There is a constant b* such that, whatever b > b* is, the deficiency process of optimal control with respect to any possible control u, i.e., the difference J T(û) - J T(u) between the optimal cost process J T(û)...

This paper is concerned with the problem of production planning in a stochastic manufacturing system with serial machines
that are subject to break-down and repair. The machine capacities are modeled by a Markov chain. The objective is to choose
the input rates at the various machines over time in order to meet the demand for the system’s productio...

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upp...

We consider a production planning problem for a general jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are modeled as Markov chains. The objective is to choose the rates of production of the final products and intermediate parts on the various machines over time in order to meet the de...

We consider the limit behavior of some functional of a Wiener process and an arbitrary absolutely continuous adapted function. This kind of functional arises in the problem of control of the linear regulator with quadratic criteria disturbed by white noise. The results obtained make it possible to prove that one cannot improve the estimate of the q...

This paper is concerned with optimal production rates for a failure-prone machine that produces two distinct part types. We consider the problem of controlling production rates so as to minimize the expected long-run average cost of product surpluses over time. We assume constant per unit holding and shortage costs and constant demand rates for the...

The stochastic linear quadratic regulator with constant coefficients is considered in continuous time when the horizon tends to infinity. It is shown that the feedback control, which is optimal for the infinite time horizon in the corresponding deterministic problem is optimal in probability for any rate function which tends to zero and almost sure...

We consider an N-machine flowshop with unreliable machines and bounds on work-in-process. Machine capacities and demand processes are finite-state Markov chains. The problem is to choose the rates of production on the machines over time to minimize the expected discounted costs of production and inventory/backlog. We show that the value function of...

The stochastic linear quadratic regulator with constant coefficients is considered in continuous time when the horizon tends to infinity. It is shown that the feedback control, which is optimal for the infinite time horizon in the corresponding deterministic problem is optimal in probability for any rate function which tends to zero and almost sure...

We consider a production planning problem for a general jobshop subject to breakdown and repair of machines and subject to lower and upper bound constraints on work-in-process. The machine capacities and demand processes are assumed to be finite state Markov chains. The problem is to choose the rates of production on the various machines over time...

In this note we provide an explicit formula for the probability distribution function of the bankruptcy time in a general consumption/investment problem involving subsistence consumption and bankruptcy penalty.

In this note it is shown how a class of optimization problems with random terminal time, such as dynamic consumption/investment problems, can be transformed to equivalent infinite horizon optimization problems, even in the presence of boundary conditions representing bankruptcy and/or terminal bequest. In important special cases of interest, the tr...

In this paper, we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the possibility of bankruptcy. Agent’s consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiable function in the general case and by a HARA-type...

In this chapter we study the consumption behavior of an agent in the dynamic framework of consumption/investment decision making that allows the presence of a subsistence consumption level and the possibility of bankruptcy. The agent’s consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differen...

In this chapter we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the presence of a subsistence consumption level and the possibility of bankruptcy. Agent’s consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differenti...

Let {X i } i=1 ∞ be a sequence of independent identically distributed random variables with a finite variance. Consider r.v.’s Z n =U n (X 1 ,⋯,X n ), where U n :ℝ n →ℝ are some functions. It is shown that under mild conditions on the sequence {U n }, there exists a numerical sequence μ n such that Z n -μ n @>P>>0.

In this note we provide an explicit formula for the probability distribution function of the bankruptcy time in a general consumption/investment problem involving subsistence consumption and bankruptcy penalty.

In this paper we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the presence of a subsistence consumption level and the possibility of bankruptcy. Agent's consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiab...

We consider a production planning problem in an N-machine flowshop subject to breakdown and repair of machines and to non-negativity constraints on work-in-process. The machine capacities and demand processes are assumed to be finite-state Markov chains. The problem is to choose the rates of production on the N machines over time to minimize the ex...

This paper studies one dimensional diffusion with controlled drift. We give definitions of an almost surely optimal policy and a policy optimal in probability. These types of optimality are much stronger than the classical optimality for the expected limiting average per unit time cost (optimality in mean on [0,∞)). To analyse when an optimal in me...

In this paper, we consider a production planning problem in an N-machine flowshop subject to breakdown and repair of machines and subject to non-negativity constraints on work-inprocess. The machine capacities and demand processes are assumed to be finite state Markov chains. The problem is to choose the rate of production over time so as to minimi...

This paper solves a general continuous-time single-agent consumption and portfolio decision problem with subsistence consumption in closed form. The analysis allows for general continuously differentiable concave utility functions. The model takes into consideration that consumption must be no smaller than a given subsistence rate and that bankrupt...

In this paper, we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the possibility of bankruptcy. Agent's consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiable function in the general case and by a HARA-type...

This book is devoted toa specific problem in the general theory of optimalcontrol -- sequential control under conditions of incomplete information. The main results concern the case in which at each moment ofn(continuous or discrete) time only a finite number of controls are admissible and the result of control action conducted in a Bayesian framew...

Although deterministic NG-models have global indexes (the N-growth rate and N-path) which the asymptotic behavior of numerous classes of optimal paths, there are no such global indexes in the stochastic case. Thus, when studying the different types of extremal problems connected, for example, with objective functions of the additive or multiplicati...

Consumption problems / Gl. v monografii "Optimal consumption and investment with bankruptcy" - Kluwer Academic publisher - Boston - Dordrecht - London, 1997.

Gl. v monografii "Optimal consumption and investment with bankruptcy", Kluwer Academic publsher, Boston - Dordrecht - London, 1997.

aversion behavior in consumption investment problems with substitent consumption and bankruptcy / Gl. v monografii "Optimal consumption and investment with bankruptcy", Kluwer Academic publisher, Boston - Dordrecht - London, 1997.

/ Automatika. 1997. V.33. ¹4.

shops / Gl. v monografii «Mathematics of Stochastic Manufacturing Systems». 1997. V.33. ¹4.

In this paper some explicit formulae for many-server queueining systems are obtained. On this basis transient phenomena corresponding to the case of heavy traffic are investigated.