1,721,020 research outputs found
An Algorithm for Equilibrium in a Dynamic Stochastic Monetary Economy
Full text linkThis paper establishes an algorithm for the equilibrium in a stochastic continuous time economy model, on a finite time interval, including a representative agent maximizing her expected total utility of consumption, leisure, and money, and a single firm that optimally produces the consumption good and maximizes its expected total profits based on employment rate and money held. First, under the assumption of equilibrium, a link between the firm’s control problem and the representative agent’s optimal expected total utility is obtained. Then such link is exploited to establish an algorithm for equilibrium
Singular Stochastic Control of a Singular Diffusion Process
No full textThis paper studies the monotone follower problem for a one-dimensional singular diffusion process. The dynamic programming principle is established. It is shown that the value function is continuous and satisfies the Hamilton-Jacobi-Bellman equation in the viscosity sens
Membro dal 2009 - Nucleo di Valutazione della ricerca e della didattica della Facoltà di Economia
No full textStochastic multicompartmental systems: a counting process approach for parameter estimation
No full textIDENTIFYING THE FREE BOUNDARY OF A STOCHASTIC, IRREVERSIBLE INVESTMENT PROBLEM VIA THE BANK-EL KAROUI REPRESENTATION THEOREM
No full textWe study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Itô diffusion controlled by a nondecreasing process representing the cumulative investment. The firm aims to maximize its expected total net profit by choosing the optimal investment process. That is a singular stochastic control problem. We derive some first order conditions for optimality, and we characterize the optimal solution in terms of the base capacity process l(t), i.e., the unique solution of a representation problem in the spirit of Bank and El Karoui [P. Bank and N. El Karoui, Ann. Probab., 32(2004), pp. 1030-1067]. We show that the base capacity is deterministic and it is identified with the free boundary ŷ(t) of the associated optimal stopping problem when the coefficients of the controlled diffusion are deterministic functions of time. This is a novelty in the literature on finite horizon singular stochastic control problems. As a subproduct this result allows us to obtain an integral equation for the free boundary, which we explicitly solve in the infinite horizon case for a Cobb-Douglas production function and constant coefficients in the controlled capacity process. © 2014 Society for Industrial and Applied Mathematics
On the Lack of Optimal Classical Stochastic Controls in a Capacity Expansion Problem
Full text linkThe stochastic control problem of a firm aiming to optimally expand the production capacity, through irreversible investment, in order to maximize the expected total profits on a finite time interval has been widely studied in the literature when the firm’s capacity is modeled as a controlled Itˆo process in which the control enters additively and it is a general nondecreasing stochastic process, possibly singular as a function of time, representing the cumulative investment up to time t. This note proves that there is no solution when the problem falls in the so-called classical control setting; that is, when the control enters the capacity process as the rate of real investment, and hence the cumulative investment up to time t is an absolutely continuous process (as a function of time). So, in a sense, this note explains the need for the larger class of nondecreasing control processes appearing in the literature
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