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Abstract: Abstract We study insider trading in a jump-binomial model of the financial market that is based on a marked binomial process and that serves as a suitable alternative to some classical trinomial models. Our investigations focus on the two main questions: measuring the advantage of the insider’s additional information and stating a closed form for her hedging strategy. Our approach is based on the results of enlargement of filtration in a discrete-time setting stated by Blanchet-Scalliet and Jeanblanc (in: From probability to finance, Springer, Berlin, 2020) and on a stochastic analysis for marked binomial processes developed in the companion paper (Halconruy in Electron J Probab 27:1–39, 2022). Our work provides in a discrete-time and an incomplete market setting the analogues of some results of Amendinger et al. (Stoch Process Appl 89(1):101–116, 2000; Finance Stoch 7(1):29–46, 2003), Imkeller et al. (1998, 2006) and extends in an insider framework some utility maximization results stated in Delbaen and Schachermayer (The mathematics of arbitrage, Springer, Berlin, 2006) and in Runggaldier et al. (in: Seminar on stochastic analysis, random fields and applications III, Springer, Berlin, 2002). PubDate: 2023-09-11
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Abstract: Abstract In the decumulation phase of a pension plan, consumption depends on the level of annuitization. We measure the welfare loss of an individual with a demand for annuitization if he has no access to annuitization or, equivalently, does not use such access. Unlike earlier studies of the value of the annuity option, both individuals with and without access to annuitization, respectively, are offered complete flexibility in the consumption/payout profile. In that sense, we assume that the financial institutions (are allowed to) design the best possible products in the two regimes, with and without annuitization. We find for realistic parameters that a patient individual with time-additive preferences loses 22% of wealth upon retirement if not annuitizing. Sensitivity studies show that the relative loss decreases with a higher interest rate, a higher market price of financial risk, a higher market price of mortality risk, more certainty in the lifetime distribution, and a lower elasticity of intertemporal substitution. Further, we analyze a suboptimal bank product based on conditional expected residual lifetime. PubDate: 2023-08-14
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Abstract: Abstract The United Nations aim to perform a transition toward a sustainable environment where people can live by decoupling economic growth from resource use. Through the definition of the Agenda 2030 and the corresponding sustainable development goals, this transition asks for a lower dependence on non-renewable resources and for the use of recycled materials in a finite term perspective. In this respect, we provide an optimal control model which searches for an efficient allocation of labor between non-recycling and recycling sectors exploiting a given non-renewable resource. The optimization process is carried out over a finite time horizon in accordance with the need of rapidly achieving the targets imposed by the ecological transition. By employing the classical tools of optimal control theory, a complete theoretical analysis of the model well-posedness is developed under the assumption of linear production in both sectors. The approach is applied in order to simulate a hypothetical test case. PubDate: 2023-08-12
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Abstract: Abstract Data envelopment analysis (DEA) is a measurement method for estimating the relative efficiency of decision-making units (DMUs) that can calculate economic (i.e., cost and revenue) efficiency levels of DMUs and can move economic activities toward the performance improvement. DEA also determines the optimal scale sizes (OSSs) of economic activities with real-valued measures in the right combination of scale and allocative efficiencies. Due to the presence of integer input–output measures in many applications, in this paper, alternative concepts of average-cost efficiency and average-revenue efficiency with integer measures are proposed. In fact, by considering the known prices of inputs (outputs), two-step models are introduced for numerically calculating the OSSs with integer inputs and outputs. In addition, the proposed methods are used for a twelve-period data set of a foundry company in Iran. The automotive industry and related industries, especially the foundry and parts manufacturing industries are among the industries that play an important role in the growth of a country's economy. Therefore, the provision of an appropriate scale to ensure their economic efficiency (cost and revenue) is necessary. The results of the investigation show that the proposed approach is practical for estimating OSSs in terms of minimizing inputs (maximizing outputs) of companies with integer input–output values. PubDate: 2023-08-12
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Abstract: Abstract We devise a theoretical model for the optimal dynamical control of an infectious disease whose diffusion is described by the SVIR compartmental model. The control is realized through implementing social rules to reduce the disease’s spread, which often implies substantial economic and social costs. We model this trade-off by introducing a functional depending on three terms: a social cost function, the cost supported by the healthcare system for the infected population, and the cost of the vaccination campaign. Using Pontryagin’s Maximum Principle, we are able to characterize the optimal control strategy in three instances of the social cost function, the linear, quadratic, and exponential models, respectively. Finally, we present a set of results on the numerical solution of the optimally controlled system by using Italian data from the recent COVID-19 pandemics for the model calibration. PubDate: 2023-08-12
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Abstract: Abstract We present two efficient low- and high-order Runge–Kutta time embedded pairs coupled with a fourth-order compact scheme in space for solving the regime-switching American options model. First, we transform the free boundary regime-switching partial differential equation (PDE) into a system of nonlinear fixed-free boundary PDEs with a multi-fixed domain. Next, we introduce a square-root function that improves the non-smoothness in the model. With the square-root function and an extrapolated Taylor series expansion, a high-order Robin boundary scheme is obtained, from which we construct an analytical approximation for computing the first derivative of the optimal exercise boundary in each regime. The optimal exercise boundary, left boundary values and time-dependent coefficient in the nonlinear model for each regime are obtained from the analytical approximation. Moreover, the coupled variables are estimated with the Hermite interpolation. Numerical experiment is conducted with several examples, and we further verified our results with the existing methods. Our proposed methodology achieved highly accurate results with little computational speed and very coarse grids. PubDate: 2023-08-02
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Abstract: Abstract This paper deals with a class of optimal control problems which arises in advertising models with Volterra Ornstein-Uhlenbeck process representing the product goodwill. Such choice of the model can be regarded as a stochastic modification of the classical Nerlove-Arrow model that allows to incorporate both presence of uncertainty and empirically observed memory effects such as carryover or distributed forgetting. We present an approach to solve such optimal control problems based on an infinite dimensional lift which allows us to recover Markov properties by formulating an optimization problem equivalent to the original one in a Hilbert space. Such technique, however, requires the Volterra kernel from the forward equation to have a representation of a particular form that may be challenging to obtain in practice. We overcome this issue for Hölder continuous kernels by approximating them with Bernstein polynomials, which turn out to enjoy a simple representation of the required type. Then we solve the optimal control problem for the forward process with approximated kernel instead of the original one and study convergence. The approach is illustrated with simulations. PubDate: 2023-07-28
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Abstract: Abstract There is a widespread interest among institutions and economic agents for a reduction of the environmental impact of the production system. An important role seems to be played by the ability of public institutions to push the transition toward a green economy also through the application of fiscal policies that envisage a system of rewards and penalties, respectively, for those companies which adopt green strategies and those which do not. It is clear that readjusting older production systems to new pollution regulations can lead in the short term to profitability reductions for the companies implementing them, even though it is possible to assume increases in profitability over medium-long time horizons. One possible approach to this issue is the classical econometric one, which analyzes the effect of different parameters of multivariate models, that influence the level of pollution due to production systems with different propensity for environmental protection. Optimal control models have been also considered with control variables relating to the technologies of production systems and public incentive policies for the green economy: see for example (Tan et al. in J Syst Sci Inf 9(1):61–73, 2021). In recent years, many scholars have studied the relationship between environmental regulation and enterprise technological innovation using evolutionary games, involving mainly economic incentives and fiscal strategies (see see Suyong et al. in Appl Math Comput 355(15):343–355, 2019; Zhang and Li in Appl Math Model 63:577–590, 2018). In our article, we propose a dynamical model where the public administration uses pollution penalties as a control variable in order to push a production sector toward better performances concerning two targets, pollution level and profitability. To this end, we consider the effects of competitiveness among firms and technology innovation. PubDate: 2023-07-15 DOI: 10.1007/s10203-023-00404-2
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Abstract: Abstract In this note, we point out a missing assumption for ‘Michael Heinrich Baumann, Beating the market' A mathematical puzzle for market efficiency, Decis Econ Finance 45: 279–325, 2022.’ In detail, we have to assume the (almost sure) survival of the controllers. Further, we discuss this assumption concerning relevance for theory and implementations and how it may alter the results and we give directions for future research. PubDate: 2023-07-06 DOI: 10.1007/s10203-023-00405-1
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Abstract: An overview is given on the use of Dini and Hadamard directional derivatives in various types of multiobjective optimization problems. Necessary optimality conditions are considered for a problem with an abstract constraint, for a problem with inequality and equality constraints and for a problem with both inequality and equality constraints and an abstract constraint. The issue of constraint qualifications is examined, and several first-order sufficient optimality conditions are presented for the third type of multiobjective optimization problems. PubDate: 2023-06-07 DOI: 10.1007/s10203-023-00403-3
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Abstract: Abstract The structure of uncertainty underlying certain decision problems may be so complex as to elude decision makers’ full understanding, curtailing their willingness to pay for payoff-relevant information—a puzzle manifesting itself in, for instance, low stock-market participation rates. I present a decision-theoretic method that enables an analyst to identify decision makers’ information-processing abilities from observing their preferences for information. A decision maker who is capable of understanding only those events that either almost always or almost never happen fails to attach instrumental value to any information source. On the other hand, non-trivial preferences for information allow perfect identification of the decision maker’s technological capacity. PubDate: 2023-06-01 DOI: 10.1007/s10203-022-00376-9
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Abstract: Abstract This paper investigates optimal investment problems in the presence of stochastic interest rates and stochastic volatility under the expected utility maximization criterion. The financial market consists of three assets: a risk-free asset, a risky asset, and zero-coupon bonds (rolling bonds). The short interest rate is assumed to follow an affine diffusion process, which includes the Vasicek and the Cox–Ingersoll–Ross (CIR) models, as special cases. The risk premium of the risky asset depends on a square-root diffusion (CIR) process, while the return rate and volatility coefficient are unspecified and possibly given by non-Markovian processes. This framework embraces the family of the state-of-the-art 4/2 stochastic volatility models and some non-Markovian models, as exceptional examples. The investor aims to maximize the expected utility of the terminal wealth for two types of utility functions, power utility, and logarithmic utility. By adopting a backward stochastic differential equation (BSDE) approach to overcome the potentially non-Markovian framework and solving two BSDEs explicitly, we derive, in closed form, the optimal investment strategies and optimal value functions. Furthermore, explicit solutions to some special cases of our model are provided. Finally, numerical examples illustrate our results under one specific case, the hybrid Vasicek-4/2 model. PubDate: 2023-06-01 DOI: 10.1007/s10203-022-00374-x
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Abstract: Abstract In this research, inverse data envelopment analysis (IDEA) approaches are proposed to measure inputs changes for output perturbations made while the convexity assumption is relaxed. Actually, inverse free disposal hull (IFDH) techniques under constant returns to scale (CRS) assumption are introduced from two perspectives, optimistic and pessimistic. In models proposed in this study, the efficiency of decision-making units (DMUs) is maintained after adding perturbed DMU with new input and output values. These inverse problems are multiobjective nonlinear that are converted to equivalent linear models and finding all Pareto efficient solutions is discussed. The models have also been tested using a real-world case study from the banking sector. The findings reveal valuable facts concerning the changes of inputs for changes of outputs from optimistic and pessimistic aspects while the convexity axiom is dropped. PubDate: 2023-06-01 DOI: 10.1007/s10203-022-00377-8
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Abstract: Abstract Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections’ outcomes, no matter how paradoxical it may appear. In this respect, we consider a set of candidates \(1, 2, \ldots , m \) and, for any subset A of \(\{1, 2, \ldots , m \}\) , we fix a ranking among the candidates belonging to A. We wonder whether it is possible to find a population of voters whose preferences, expressed according to the Condorcet’s proposal, give rise to that family of rankings. We will show that, whatever be such family, a population of voters can be constructed that realize all the rankings of it. Our conclusions are similar to those coming from D. Saari’s results. Our results are, however, constructive and allow for the study of quantitative aspects of the wanted voters’ populations. PubDate: 2023-04-07 DOI: 10.1007/s10203-023-00393-2
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Abstract: Abstract ‘All models are wrong but some are useful’ Box (Robustness in statistics, Elsevier, pp 201–236, 1979). But, how to find those useful ones starting from an imperfect model' How to make informed data-driven decisions equipped with an imperfect model' These fundamental questions appear to be pervasive in virtually all empirical fields—including economics, finance, marketing, healthcare, climate change, defense planning, and operations research. This article presents a modern approach (builds on two core ideas: abductive thinking and density-sharpening principle) and practical guidelines to tackle these issues in a systematic manner. PubDate: 2023-03-30 DOI: 10.1007/s10203-023-00390-5
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Abstract: Abstract We extend the dynamic Cournot duopoly framework with emission charges on output by Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), which encompassed homogeneous products in its original formulation, to the more general case of differentiated goods, in order to highlight the richness in its static and dynamic outcomes. Each firm is taxed proportionally to its own emission only and charge functions are quadratic. Moreover, due to an adjustment capacity constraint, firms partially modify their output level toward the best response. Like in Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), the only steady state coincides with the Nash equilibrium, and it will be considered admissible when it guarantees the positivity of the marginal emission charge. We find that the full efficacy of the environmental policy, which applies to an equilibrium that is globally asymptotically stable anytime it is admissible, is achieved in the case of independent goods, as well as with a low good interdependence degree in absolute value, independently of being substitutes or complements. When goods are substitutes and their interdependence degree is high, the considered environmental policy is still able to reduce pollution at the equilibrium, but the latter is stable just when the policy intensity degree is large enough. When instead goods are complements and their interdependence degree is high in absolute value, the considered environmental policy produces detrimental effects on the pollution level and the unique equilibrium is always unstable, when admissible. This highlights that, from the static viewpoint, even in the absence of free riding possibilities, the choice of the mechanism to implement has to be carefully pondered, according to the features of the considered economy. PubDate: 2023-03-01 DOI: 10.1007/s10203-023-00387-0
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Abstract: Abstract The game value of a pursuit-evasion differential game is an estimation of the game’s payoff at the instant when all the players employ their optimal strategies. In this paper, we estimate this value for a fixed duration differential game problem of countably many pursuers and one evader with the Grönwall-type constraints, a generalization of the well known geometric constraints, imposed on all the players’ control functions. The players’ dynamics are governed by a generalized dynamic equations. We construct the attainability domain and a Grönwall-type optimal strategies for the players. The constructed strategies are then employed in establishing that the estimated game value is guaranteed for the players. PubDate: 2023-02-22 DOI: 10.1007/s10203-023-00389-y
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Abstract: Abstract We consider a dynamic principal–agent model that naturally extends the classical Holmström–Milgrom setting to include a risk capable of stopping production completely. We obtain an explicit characterization of the optimal wage along with the optimal action provided by the agent. The optimal contract is linear by offering both a fixed share of the output which is similar to the standard Holmström–Milgrom model and a linear prevention mechanism that is proportional to the random lifetime of the contract. We then extend the model by allowing insurable risks where the agent can control the intensity of the failure by exerting an additional costly effort. PubDate: 2023-02-10 DOI: 10.1007/s10203-023-00386-1
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Abstract: Abstract Equilibrium is a central concept in numerous disciplines including economics, management science, operations research, and engineering. We are concerned with an evolutionary quasivariational inequality which is connected to discrete dynamic competitive economic equilibrium problem in terms of maximization of utility functions and of excess demand functions. We study the discrete equilibrium problem by means of a discrete time-dependent quasivariational inequality in the discrete space \(\ell ^2([0,T]_{\mathbb {Z}},\mathbb {R})\) . We ensure an existence result of discrete time-dependent equilibrium solutions. Finally, we show the stability of equilibrium in a completely decentralized Walrasian general equilibrium economy in which prices are fully controlled by economic agents, with production and trade occurring out of equilibrium. PubDate: 2023-01-24 DOI: 10.1007/s10203-022-00385-8
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Abstract: Abstract We investigate the evaluation problem of variable annuities by considering guaranteed minimum maturity benefits, with constant or path-dependent guarantees of up-and-out barrier and lookback type, and guaranteed minimum accumulation benefit riders, with different forms of the surrender amount. We propose to solve the non-standard Volterra integral equations associated with the policy valuations through a randomized trapezoidal quadrature rule combined with an interpolation technique. Such a rule improves the converge rate with respect to the classical trapezoidal quadrature, while the interpolation technique allows us to obtain an efficient algorithm that produces a very accurate approximation of the early exercise boundary. The method accuracy is assessed by constructing two benchmarks: The first one, developed in a lattice framework, is characterized by a novel algorithm for the lookback path-dependent guarantee obtained thanks to the lattice convergence properties, while the application is straightforward in the other cases; the second one is based on the least-squares Monte Carlo simulations. PubDate: 2023-01-02 DOI: 10.1007/s10203-022-00383-w
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