We consider a firm expanding its production capacity in stages under uncertainty. The firm decides on the investment times and the size of the investment lumps. This setting gives rise to an impulse ...control problem for which we derive a quasi-variational inequality that involves two state variables: a stochastic price process and a controlled capacity process. We provide a general verification theorem and construct an optimal two-dimensional (
s
,
S
)-type policy for a specific case. The firm “waits and sees” before investing until the perpetuity value of newly installed capacity exceeds the total opportunity cost by a sufficient margin. Our model generalizes extant models dealing with “the option to expand” capacity and makes predictions of both the optimal investment timing and the optimal scale of production.
This paper considers a firm’s capacity expansion decisions under uncertainty. The firm has leeway in timing investments and in choosing how much capacity to install at each investment time. We model this problem as the sequential exercising of compound capacity expansion options with embedded optimal capacity choices. We employ the impulse control methodology and obtain a quasi-variational inequality that involves two state variables: an exogenous, stochastic price process and a controlled capacity process (without a diffusion term). We provide a general verification theorem and identify—and prove the optimality of—a two-dimensional
(
s
,
S
)
-type policy for a specific (admittedly restrictive) choice of the model parameters and of the running profit. The firm delays investment in capacity to ensure that the perpetuity value of newly installed capacity exceeds the total opportunity cost, including the fixed cost component, by a sufficient margin. Our general model for “the option to expand” transcends a single-option exercise and yields predictions of both the optimal investment timing and the optimal scale of production.
On the interpretation of the Master Equation Bensoussan, A.; Frehse, J.; Yam, S.C.P.
Stochastic processes and their applications,
July 2017, 2017-07-00, Letnik:
127, Številka:
7
Journal Article
Recenzirano
Odprti dostop
Since its introduction by P.L. Lions in his lectures and seminars at the College de France, see Lions 6, and also the very helpful notes of Cardialaguet (2013) on Lions’ lectures, the Master Equation ...has attracted a lot of interest, and various points of view have been expressed, see for example Carmona and Delarue (2014), Bensoussan et al. (2015), Buckdahn et al. 3. There are several ways to introduce this type of equation; and in those mentioned works, they involve an argument which is a probability measure, while P.L. Lions has recently proposed the alternative idea of working on the Hilbert space of square integrable random variables. Hence writing the equation is an issue; while another issue is its origin. In this article, we discuss all these various aspects. An important reference is the seminar at College de France delivered by P.L. Lions on November 14, 2014.
This paper studies the issue of coordinating equipment maintenance operations with capital investment strategy in the presence of random equipment failures. The traditional approach, developed by ...Kamien and Schwartz (KS) in their celebrated paper published in 1971, is to formulate the problem as a deterministic optimal control problem with the probability of machine failure as the state variable. With this approach, the optimal policy is deterministic. As a major departure from the KS approach, we explicitly model the underlying stochastic process of machine failures. Our analysis of the stochastic dynamic programming model offers new insights into the problem. Under a long planning horizon with a limited replacement opportunity, each individual machine serves as a
revenue generator
and contributes a significant amount to the profit of the system. In contrast, when the replacement budget is quite generous over a relatively short planning horizon, adding one extra machine only helps as a
backup
for unexpected failures of the machines purchased before it. An interesting result derived from this comparison is that a deterministic policy turns out to be optimal for the former, while a state-contingent policy must be applied to the latter. In other words, the deterministic KS approach does not work in general when a chain of machine replacement is considered. We further characterize the effects of the discount rate, productivity deterioration, learning, decision delay, and technology advancement on the optimal policy.
Electrical behavior of commercial off-the-shelf normally-off GaN power transistors under heavy ion irradiation is presented based on technology computer aided design numerical simulation in order to ...better understand the mechanism of single event effects (SEEs) in these devices. First, the worst case has been defined from the single event transient mechanism. Then, the decrease in the electric field observed after irradiation and the traps effect have been addressed. Finally, possible mechanisms of SEE in these devices under heavy ion are proposed.
Linear-Quadratic Mean Field Games Bensoussan, A.; Sung, K. C. J.; Yam, S. C. P. ...
Journal of optimization theory and applications,
05/2016, Letnik:
169, Številka:
2
Journal Article
Recenzirano
Odprti dostop
We provide a comprehensive study of a general class of linear-quadratic mean field games. We adopt the adjoint equation approach to investigate the unique existence of their equilibrium strategies. ...Due to the linearity of the adjoint equations, the optimal mean field term satisfies a forward–backward ordinary differential equation. For the one-dimensional case, we establish the unique existence of the equilibrium strategy. For a dimension greater than one, by applying the Banach fixed point theorem under a suitable norm, a sufficient condition for the unique existence of the equilibrium strategy is provided, which is independent of the coefficients of controls in the underlying dynamics and is always satisfied whenever the coefficients of the mean field term are vanished, and hence, our theories include the classical linear-quadratic stochastic control problems as special cases. As a by-product, we also establish a neat and instructive sufficient condition, which is apparently absent in the literature and only depends on coefficients, for the unique existence of the solution for a class of nonsymmetric Riccati equations. Numerical examples of nonexistence of the equilibrium strategy will also be illustrated. Finally, a similar approach has been adopted to study the linear-quadratic mean field type stochastic control problems and their comparisons with mean field games.
1. Monoclonal antibodies targeting tumors are one of the most important discoveries in the field of cancer therapy in the last decade.
2. A lack of Natural Killer cells observed in many cancers may ...therefore be a cause of the low efficacy of antibodies observed in some clinical situations.
3. The ways to enhance the ADCC mechanism and the perspective of the treatment with therapeutic antibodies : enhancement of CD16 expression by cytokines or anti-CD137 antibody
4. A combination of NK cell adoptive immunotherapy and monoclonal antibodies may overcome the resistance to the treatment and enhance their efficacy.
Display omitted
•Therapeutic antibodies are used to treat solid tumors and hematologic malignancies.•A lack of Natural killer cells diminishes the antibody efficacy against the tumor.•NK cells combined with antibodies can overcome a resistance to the antibody.•Cytokine use or preventing CD16 shedding may potentialize the NK cell efficacy.
Monoclonal antibodies targeting tumors are one of the most important discoveries in the field of cancer. Although several effective antibodies have been developed, a relapse may occur. One of their mechanisms of action is Antibody Dependent Cell Cytotoxicity (ADCC), by engaging the Fc γ receptor CD16 expressing Natural Killer cells, innate lymphoid cells involved in cancer immunosurveillance and able to kill tumor cells. A lack of NK cells observed in many cancers may therefore be a cause of the low efficacy of antibodies observed in some clinical situations. Here we review clear evidences of the essential partnership between NK cells and antibodies showed in vitro, in vivo, and in clinical trials in different indications, describe the hurdles and ways to enhance ADCC and the evolution of monoclonal antibody therapy. NK cell adoptive immunotherapy combined with monoclonal antibodies may overcome the resistance to the treatment and enhance their efficacy.
A New Approach to Contract Design with Private Inventory Information In a typical decentralized supply chain, a downstream retailer privately observes its inventory level and has an informational ...advantage over the upstream supplier. In “A Stationary Infinite-Horizon Supply Contract Under Asymmetric Inventory Information” by Bensoussan, Sethi, and Wang, the authors study how to optimally design a stationary, truth-telling, long-term contract in such a setting. In contrast to the classic first order approach in literature, they formulate the contract design as an optimization over a functional space and develop a solution approach based on the calculus of variations. They further apply their necessary optimality condition to the class of batch-order contracts, which replenish a prespecified inventory quantity for a fixed payment in each period only when the retailer has zero inventory on hand.
We consider a decentralized supply chain in which a supplier sells goods to a retailer facing general random demand over an infinite horizon. The retailer satisfies the demand to the extent of the inventory on hand. The retailer has private information about the retailer’s stock in each period, and the supplier offers the retailer a supply contract menu to account for the information asymmetry. We obtain a necessary condition for optimizing a long-term stationary truth-telling contract under general demand and belief distributions. We apply it to a batch-order contract, which replenishes a prespecified inventory quantity for a fixed payment in each period only when the retailer’s beginning inventory becomes zero. Methodologically, we formulate the supplier’s contract design as a calculus of variations problem and apply the concept of Gâteaux derivative to obtain these results. This methodology can potentially be applied to other dynamic contracting problems. Funding: A. Bensoussan acknowledges support from the National Science Foundation Grant NSF-DMS 220 47 95. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2020.0495 .
As well studied in the operations research literature, optimization of a mutual reserve system (e.g., federal reserves) and a nonmutual one such as regular inventory systems requires solving ...simultaneous systems of quasi-variational inequalities, of which analytical solutions in closed form remain unattainable and computational solutions are still intractable. Thus far, the studies of reserve optimization are of intra-nations (e.g., central bank reserves) as opposed to inter-nations (e.g., COVID vaccine reserves of the United Nations). In this paper, we advance a method of computational analytics for mutual reserve optimization, with an international perspective in response to the intensifying challenge on global medical reserves during the COVID pandemic. A solution algorithm is developed in the context of maritime mutual insurances (a long existent international mutual reserve system) and then tested through comprehensive numerical experiments.
In this paper, we develop a splitting solution method for two-sided impulse control of Brownian motion, which leads to an expanding range of band control applications and studies, such as monetary reserves (including the previously studied cash management problem, exchange rate control in central banks, and marine mutual insurance reserves), inventory systems, and lately natural resources and energy reservation. It has been shown since earlier studies in 1970s that the optimal two-sided impulse control can be characterized by a two-band control policy of four parameters Formula: see text with Formula: see text, of which the dynamic programming characteristics leads to a quasi-variational inequality (QVI) with two sides. Thus far, the focus of band control problems has been on determination of optimal band policy parameters. Its solution methods, as far as we can ascertain from the current literature, have centered on finding the four parameters by solving simultaneously characteristic systems of QVI inequalities, of which analytical solutions of closed form remain unattainable and computational solutions are still largely intractable. The key contributions of this paper are (1) development of a splitting method of decomposing a general two-sided band control problem into two iterative one-sided band control problems, each iteration being reduced to a one-dimension optimization; (2) obtaining a theorem on geometrical characterization of band-splitting control, including QVI and computational analytics and characteristics of band-splitting functions and solutions; and (3) development of a band-splitting solution algorithm for the two-sided impulse control, including an effective initial-point selection method that is termed the separate approximation of geometric conditions method. Numerical comparison experiments are carried out to validate and test the effectiveness and accuracy of the splitting solution method. The method is not only computationally effective, but also useful for proving theoretical results. Funding: A. Bensoussan is supported in part by the National Science Foundation Grant DMS-2204795. The study was supported by the General Research Fund Grants 5230/06E and 5225/07E, both of which J. J. Liu was the principal investigator as chair professor of maritime studies, and was based on the PhD thesis of J. Yuan, who was jointly supervised by A. Bensoussan, all at Hong Kong Polytechnic University. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2011.0427 .
As well studied in the operations research literature, optimization of a mutual reserve system (e.g., federal reserves) and a nonmutual one such as regular inventory systems requires solving ...simultaneous systems of quasi-variational inequalities, of which analytical solutions in closed form remain unattainable and computational solutions are still intractable. Thus far, the studies of reserve optimization are of intra-nations (e.g., central bank reserves) as opposed to inter-nations (e.g., COVID vaccine reserves of the United Nations). In this paper, we advance a method of computational analytics for mutual reserve optimization, with an international perspective in response to the intensifying challenge on global medical reserves during the COVID pandemic. A solution algorithm is developed in the context of maritime mutual insurances (a long existent international mutual reserve system) and then tested through comprehensive numerical experiments.
In this paper, we develop a splitting solution method for two-sided impulse control of Brownian motion, which leads to an expanding range of band control applications and studies, such as monetary reserves (including the previously studied cash management problem, exchange rate control in central banks, and marine mutual insurance reserves), inventory systems, and lately natural resources and energy reservation. It has been shown since earlier studies in 1970s that the optimal two-sided impulse control can be characterized by a two-band control policy of four parameters Formula: see text with Formula: see text, of which the dynamic programming characteristics leads to a quasi-variational inequality (QVI) with two sides. Thus far, the focus of band control problems has been on determination of optimal band policy parameters. Its solution methods, as far as we can ascertain from the current literature, have centered on finding the four parameters by solving simultaneously characteristic systems of QVI inequalities, of which analytical solutions of closed form remain unattainable and computational solutions are still largely intractable. The key contributions of this paper are (1) development of a splitting method of decomposing a general two-sided band control problem into two iterative one-sided band control problems, each iteration being reduced to a one-dimension optimization; (2) obtaining a theorem on geometrical characterization of band-splitting control, including QVI and computational analytics and characteristics of band-splitting functions and solutions; and (3) development of a band-splitting solution algorithm for the two-sided impulse control, including an effective initial-point selection method that is termed the separate approximation of geometric conditions method. Numerical comparison experiments are carried out to validate and test the effectiveness and accuracy of the splitting solution method. The method is not only computationally effective, but also useful for proving theoretical results.
Funding: A. Bensoussan is supported in part by the National Science Foundation Grant DMS-2204795. The study was supported by the General Research Fund Grants 5230/06E and 5225/07E, both of which J. J. Liu was the principal investigator as chair professor of maritime studies, and was based on the PhD thesis of J. Yuan, who was jointly supervised by A. Bensoussan, all at Hong Kong Polytechnic University.
Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2011.427 .
In‐office subglottic intralesional steroid injections (SILSI) have gained popularity as an adjunct to operating room dilation in the treatment of subglottic stenosis. They are generally thought to ...have a low risk profile for development of systemic side effects. Here, we present a case of a 55 year old woman who developed symptoms of Cushing syndrome after receiving SILSI, including weight gain, striae, dorsal hump and alopecia. This case illustrates that despite the localized nature of SILSI, there is still a risk of developing systemic effects as a result of the treatment. Laryngoscope, 132:942–943, 2022
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