1,720,982 research outputs found
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
A unifying view on the irreversible investment exercise boundary in a stochastic, time-inhomogeneous capacity expansion problem
Full text linkThis paper studies the investment exercise boundary erasing in a stochastic, continuous time capacity expansion problem with irreversible investment on the finite time interval and a state dependent scrap value associated with the production facility at the finite horizon . The capacity process is a time-inhomogeneous diffusion in which a monotone nondecreasing, possibly singular, process representing the cumulative investment enters additively. The levels of capacity, employment and operating capital contribute to the firm's production and are optimally chosen in order to maximize the expected total discounted profits. Two different approaches are employed to study and characterize the boundary. From one side, some first order condition are solved by using the Bank and El Karoui Representation Theorem, and that sheds further light on the connection between the threshold which the optimal policy of the singular stochastic control problem activates at and the optional solution of Representation Theorem. Its application in the presence of the scrap value is new. It is accomplished by a suitable fictitious extension to of the firm's horizon and a devise to overcome the difficulties due to the presence of a non integral term in the maximizing functional. The optimal investment process is shown to become active at the so-called ``base capacity'' level, which is given as the unique solution of an integral equation. On the other hand, when the coefficients of the uncontrolled capacity process are deterministic, the optimal stopping problem classically associated to the original capacity problem is resumed and, without invoking variational teckniques but only by means of probabilistic methods, some essential properties of the investment exercise boundary, the ``free boundary'' of its continuation region, are obtained. Despite the lack of knowledge of boundary's continuity, the optimal investment process is proved to be continuous, except for a possible initial jump. Finally, unifying approaches and views, the exercise boundary is shown to coincide with the base capacity, and hence it is characterized by an integral equation not requiring any a priori regularity
An Analytical Study of Participating Policies with Minimum Rate Guarantee and Surrender Option
Full text linkWe perform a detailed theoretical study of the value of a class of participating policies with four key features: (i) the policyholder is guaranteed a minimum interest rate on the policy reserve; (ii) the contract can be terminated by the holder at any time until maturity (surrender option); (iii) at the maturity (or upon surrender) a bonus can be credited to the holder if the portfolio backing the policy outperforms the current policy reserve; (iv) due to solvency requirements the contract ends if the value of the underlying portfolio of assets falls below the policy reserve.
Our analysis is probabilistic and it relies on optimal stopping and free boundary theory. We find a structure of the optimal surrender strategy which was undetected by previous (mostly numerical) studies on the same topic. Optimal surrender of the contract is triggered by two `stop-loss' boundaries and by a `too-good-to-persist' boundary (in the language of cite{EV20}). Financial implications of this strategy are discussed in detail and supported by extensive numerical experiments
Optimal Stopping of a Hilbert Space valued Diffusion: an Infinite Dimensional Variational Inequality
Full text linkA finite horizon optimal stopping problem for an infinite dimensional diffusion X is analyzed by means of variational techniques. The diffusion is driven by a SDE on a Hilbert space H with a non-linear diffusion coefficient σ(X) and a generic unbounded operator A in the drift term. When the gain function is time-dependent and fulfils mild regularity assumptions, the value function U of the optimal stopping problem is shown to solve an infinite-dimensional, parabolic, degenerate variational inequality on an unbounded domain. Once the coefficient σ(X) is specified, the solution of the variational problem is found in a suitable Banach space V fully characterized in terms of a Gaussian measure μ. This work provides the infinite-dimensional counterpart, in the spirit of Bensoussan and Lions (Application of variational inequalities in stochastic control, 1982), of well-known results on optimal stopping theory and variational inequalities in Rn. These results may be useful in several fields, as in
mathematical finance when pricing American options in the HJM model
Analytical Pricing of American Put Options on a Zero Coupon Bond in the Heath-Jarrow-Morton Model
Full text linkWe study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in Musiela’s parametrization of the Heath–Jarrow–Morton (HJM) model for forward interest
rates. First we show regularity properties of the price function by probabilistic methods. Then we find an infinite dimensional variational formulation of the pricing problem by approximating the original optimal stopping problem by finite dimensional ones, after a suitable smoothing of the payoff. As expected, the first time the price of the American bond option equals the payoff is shown to be optimal. c 2014 Elsevier B.V. All rights reserved
Optimal dynamic procurement policies for a storable commodity with Lévy prices and convex holding costs
Full text linkIn this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm’s optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic ‘monotone follower problem’). We assume a general exponential Lévy process for the commodity’s spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a base inventory process; that is, a minimal time-dependent desirable inventory level that the firm’s manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static “newsvendor” strategy
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
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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