Subjects -> STATISTICS (Total: 130 journals)
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 Decisions in Economics and FinanceJournal Prestige (SJR): 0.116 Number of Followers: 15      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1129-6569 - ISSN (Online) 1593-8883 Published by Springer-Verlag  [2467 journals]
• Inverse data envelopment analysis without convexity: double frontiers

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: 2022-11-25

• Introduction to the Milestones series

PubDate: 2022-11-18

• Bipartite choices

Abstract: Abstract This piece in the Milestones series is dedicated to the paper coauthored by David Gale and Lloyd Shapley and published in 1962 under the title “College admissions and the stability of marriage” on the American Mathematical Monthly.
PubDate: 2022-11-16

• Optimality and duality in nonsmooth semi-infinite optimization, using a
weak constraint qualification

Abstract: Abstract Variational analysis, a subject that has been vigorously developing for the past 40 years, has proven itself to be extremely effective at describing nonsmooth phenomenon. The Clarke subdifferential (or generalized gradient) and the limiting subdifferential of a function are the earliest and most widely used constructions of the subject. A key distinction between these two notions is that, in contrast to the limiting subdifferential, the Clarke subdifferential is always convex. From a computational point of view, convexity of the Clarke subdifferential is a great virtue. We consider a nonsmooth multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints. First, we introduce the weak Slater constraint qualification and derive the Karush–Kuhn–Tucker types necessary and sufficient conditions for (weakly, properly) efficient solution of the considered problem. Then, we introduce two duals of Mond–Weir type for the problem and present (weak and strong) duality results for them. All results are given in terms of Clarke subdifferential.
PubDate: 2022-11-09

• Two representations of information structures and their comparisons

Abstract: Abstract This paper compares two representations of informativeness.
PubDate: 2022-11-02

• The robustness of the generalized Gini index

Abstract: Abstract In this paper, we introduce a map $$\varPhi$$ , which we call zonoid map, from the space of all non-negative, finite Borel measures on $${\mathbb {R}}^n$$ with finite first moment to the space of zonoids of $${\mathbb {R}}^n$$ . This map, connecting Borel measure theory with zonoids theory, allows to slightly generalize the Gini volume introduced, in the context of Industrial Economics, by Dosi (J Ind Econ 4:875–907, 2016). This volume, based on the geometric notion of zonoid, is introduced as a measure of heterogeneity among firms in an industry and it turned out to be a quite interesting index as it is a multidimensional generalization of the well-known and broadly used Gini index. By exploiting the mathematical context offered by our definition, we prove the continuity of the map $$\varPhi$$ which, in turn, allows to prove the validity of a SLLN-type theorem for our generalized Gini index and, hence, for the Gini volume. Both results, the continuity of $$\varPhi$$ and the SLLN theorem, are particularly useful when dealing with a huge amount of multidimensional data.
PubDate: 2022-10-25

• Cognitive limits and preferences for information

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: 2022-10-14

• Utility maximization in a stochastic affine interest rate and CIR risk

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: 2022-09-20

• Equalizing solutions for bankruptcy problems revisited

Abstract: Abstract When solving bankruptcy problems through equalizing solutions, agents with small claims prefer to distribute the estate according to the Constrained Equal Awards solution, while the adoption of the Constrained Equal Losses solution is preferred by agents with high claims. Therefore, the determination of which is the central claimant, as a reference to distinguish the agents with a high claim from those with a low claim, is a relevant question when designing hybrid solutions, or new methods to distribute the available estate in a bankruptcy problem. We explore the relationship between the equal awards parameter $$\lambda$$ and the equal losses parameter $$\mu$$ that characterize the two solutions. We show that the central claimant is fully determined by these parameters. In addition, we explore how to compute these parameters and present optimization problems that provide the Constrained Equal Awards and the Constrained Equal Losses solutions.
PubDate: 2022-09-02
DOI: 10.1007/s10203-022-00373-y

• Dangerous tangents: an application of $$\Gamma$$ Γ -convergence to the
control of dynamical systems

Abstract: Abstract Inspired by the classical riot model proposed by Granovetter in 1978, we consider a parametric stochastic dynamical system that describes the collective behavior of a large population of interacting agents. By controlling a parameter, a policy maker seeks to minimize her own disutility, which in turn depends on the steady state of the system. We show that this economically sensible optimization is ill-posed and illustrate a novel way to tackle this practical and formal issue. Our approach is based on the $$\Gamma$$ -convergence of a sequence of mean-regularized instances of the original problem. The corresponding minimum points converge toward a unique value that intuitively is the solution of the original ill-posed problem. Notably, to the best of our knowledge, this is one of the first applications of $$\Gamma$$ -convergence in economics.
PubDate: 2022-07-02
DOI: 10.1007/s10203-022-00372-z

• Correction to: Semi-analytical prices for lookback and barrier options
under the Heston model

Abstract: Abstract In this note, we point out a mistake in Theorem 1 of De De Gennaro Aquino and Bernard (Decis Econ Finance 42(2):715–741, 2019) and provide some missing references where the problem of pricing barrier options under the Heston model had previously been discussed.
PubDate: 2022-06-01
DOI: 10.1007/s10203-021-00360-9

• Portfolio choice in the model of expected utility with a safety-first
component

Abstract: Abstract The standard problem of portfolio choice between one risky and one riskless asset is analyzed in the model of expected utility with a safety-first component that is represented by the probability of final wealth exceeding a “safety” wealth level. It finds that a positive expected excess return remains sufficient for investing a positive amount in the risky asset except in the special situation where the safety wealth level coincides with the wealth obtained when the entire initial wealth is invested in the riskless asset. In this situation, the optimal amount invested in the risky asset is zero if the weight on the safety-first component is sufficiently large. Comparative statics analysis reveals that whether the optimal amount invested in the risky asset becomes smaller as the weight on the safety-first component increases depends on whether the safety wealth level is below the wealth obtained when the entire initial wealth is invested in the riskless asset. Further comparative statics analyses with respect to the safety wealth level and the degree of risk aversion in the expected utility component are also conducted.
PubDate: 2022-06-01
DOI: 10.1007/s10203-021-00347-6

• Beating the market' A mathematical puzzle for market efficiency

PubDate: 2022-06-01
DOI: 10.1007/s10203-021-00361-8

• Option pricing: a yet simpler approach

Abstract: Abstract We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox–Ross–Rubinstein (CRR) pricing model. The main tool used in this paper for simplifying the reasoning is applying static hedging arguments. In applying the static hedging principle, we consider Arrow–Debreu securities and digital options, or backward random processes. In the last case, the CRR model is extended to an infinite state space which leads to an interesting new phenomenon not present in the classical CRR model. At the end, we discuss the paradox involving the drift parameter $$\mu$$ in the Black–Scholes–Merton model pricing. We provide sensitivity analysis and an approximation of the speed of convergence for the asymptotically vanishing effect of drift in prices.
PubDate: 2022-06-01
DOI: 10.1007/s10203-021-00338-7

• A new class of multidimensional Wishart-based hybrid models

Abstract: Abstract In this article, we present a new class of pricing models that extend the application of Wishart processes to the so-called stochastic local volatility (or hybrid) pricing paradigm. This approach combines the advantages of local and stochastic volatility models. Despite the growing interest on the topic, however, it seems that no particular attention has been paid to the use of multidimensional specifications for the stochastic volatility component. Our work tries to fill the gap: we introduce two hybrid models in which the stochastic volatility dynamics is described by means of a Wishart process. The proposed parametrizations not only preserve the desirable features of existing Wishart-based models but significantly enhance the ability of reproducing market prices of vanilla options.
PubDate: 2022-06-01
DOI: 10.1007/s10203-021-00357-4

• Expressions of forward starting option price in Hull–White
stochastic volatility model

Abstract: Abstract We are interested in problems related to forward starting options for Hull–White stochastic volatility model. Our objective is to obtain analytical, semi-analytical, or approximated expressions of its price for simulation. To obtain an analytical representation of the price, we use Yor’s formula. However, the analytical formula is difficult to implement. Next we consider semi-analytical expressions for the price. In order to have them, we use the tower property for conditional expectations with a certain filtration and explicitly calculate it. Then, we consider an expansion expression for the price using the semi-analytical expression to have a simple expression. The semi-analytical expressions and the expansion expression can reduce computational costs and standard errors when the Monte Carlo method is used. Finally, some numerical results are given to show their accuracy and efficiency.
PubDate: 2022-06-01
DOI: 10.1007/s10203-021-00343-w

• Production and hedging under correlated price and background risks

Abstract: Abstract This paper examines the competitive firm that has to make its production and hedging decisions under correlated price and background risks. The background risk can be either financial or non-financial, which is accommodated by using a bivariate utility function. The separation theorem is shown to hold in that the firm’s optimal output level depends neither on the firm’s bivariate utility function nor on the joint distribution of the price and background risks. We derive necessary and sufficient conditions under which the firm optimally opts for an over-hedge (under-hedge). We further derive necessary and sufficient conditions under which hedging has positive (negative) effect on the firm’s optimal output level. These conditions are shown to be related to the concept of expectation dependence and bivariate preferences that include correlation aversion (correlation loving) and cross-prudence (cross-imprudence).
PubDate: 2022-06-01
DOI: 10.1007/s10203-021-00362-7

• Monetary risk measures for stochastic processes via Orlicz duality

Abstract: Abstract In this article, we extend the framework of monetary risk measures for stochastic processes to account for heavy tailed distributions of random cash flows evolving over a fixed trading horizon. To this end, we transfer the $$L^p$$ -duality underlying the representation of monetary risk measures to a more flexible Orlicz duality, in spaces of stochastic processes modelling random future evolution of financial values in continuous time over a finite horizon. This contributes, on the one hand, to the theory of real-valued monetary risk measures for processes and, on the other hand, supports a new representation of acceptability indices of financial performance.
PubDate: 2022-06-01
DOI: 10.1007/s10203-021-00334-x

• A flexible lattice framework for valuing options on assets paying discrete
dividends and variable annuities embedding GMWB riders

Abstract: Abstract In a market where a stochastic interest rate component characterizes asset dynamics, we propose a flexible lattice framework to evaluate and manage options on equities paying discrete dividends and variable annuities presenting some provisions, like a guaranteed minimum withdrawal benefit. The framework is flexible in that it allows to combine financial and demographic risk, to embed in the contract early exercise features, and to choose the dynamics for interest rates and traded assets. A computational problem arises when each dividend (when valuing an option) or withdrawal (when valuing a variable annuity) is paid, because the lattice lacks its recombining structure. The proposed model overcomes this problem associating with each node of the lattice a set of representative values of the underlying asset (when valuing an option) or of the personal subaccount (when valuing a variable annuity) chosen among all the possible ones realized at that node. Extensive numerical experiments confirm the model accuracy and efficiency.
PubDate: 2022-05-27
DOI: 10.1007/s10203-022-00371-0

• Performance measurement with expectiles

Abstract: Abstract Financial performance evaluation is intimately linked to risk measurement methodologies. There exists a well-developed literature on axiomatic and operational characterization of measures of performance. Hinged on the duality between coherent risk measures and reward associated with investment strategies, we investigate representation of acceptability indices of performance using expectile-based risk measures that recently attracted a lot of attention inside the financial and actuarial community. We propose two purely expectile-based performance ratios other than the classical gain-loss ratio and the Omega ratio. We complement our analysis with elicitability of expectile-based acceptability indices and their conditional version accounting for new information flow.
PubDate: 2022-05-19
DOI: 10.1007/s10203-022-00369-8

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