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]
• Quasivariational inequalities for dynamic competitive economic equilibrium
problems in discrete time

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

representative agents

Abstract: Abstract This paper focuses on defined-benefit pension funds in which heterogeneous plan members differ in age, salary, contribution rate, and other characteristics. The co-variation of these characteristics proves to have an important effect on the management of the fund. For example, we find that members’ ages and salary growths, if co-vary in unfavourable way, can substantially increase the funds’ liability, which in turn drives up the amount of funding required and the proportion of risky investment. This coupling effect of heterogeneity is demonstrated first through analytical statements which we derive under a simplified assumption of no investment constraints. In constrained cases for which analytical solutions are unavailable, we develop a numerical method that finds the heterogeneity-adjusted management decisions using a so-called adaptive representative agent (ARA), whose characterization is given explicitly in a key theorem. Whereas traditional methods often suffer from numerical complexity that grows exponentially with the number of heterogeneous members, the computational cost of the proposed ARA method is only linear in the number of time steps. This advantage of the ARA method and its ability to rectify the coupling effects of heterogeneity are demonstrated through our numerical example.
PubDate: 2023-01-07

• Surrender and path-dependent guarantees in variable annuities: integral
equation solutions and benchmark methods

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

• Locally-coherent multi-population mortality modelling via neural networks

Abstract: Abstract This manuscript proposes an approach for large-scale mortality modelling and forecasting with the assumption of locally-coherence of the mortality forecasts. In general, the coherence prevents diverging long-term mortality forecasts between two or more populations. Despite being considered a desirable property in a multi-population modelling framework, it could be perceived as a strong assumption when a large collection of countries is considered. We propose a neural network model which requires the coherence of the mortality forecasts only within sub-groups of similar populations. The architecture is designed to be easily interpretable and induces the creation of some clusters of countries with similar mortality patterns. This aspect also makes the model an interesting tool for analysing similarities and differences between different countries’ mortality dynamics and identifying opportunities for longevity risk diversification and mitigation. An extensive set of numerical experiments performed using all the available data from the Human Mortality Database shows that our model produces more accurate mortality forecasts with respect to some well-known stochastic mortality models. Furthermore, a massive reduction of the parameters to optimise is achieved with respect to the benchmark mortality models.
PubDate: 2022-12-29

• 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
DOI: 10.1007/s10203-022-00375-w

• Two representations of information structures and their comparisons

Abstract: Abstract This paper compares two representations of informativeness.
PubDate: 2022-11-02
DOI: 10.1007/s10203-022-00379-6

• 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
DOI: 10.1007/s10203-022-00378-7

• 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
DOI: 10.1007/s10203-022-00376-9

• 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
DOI: 10.1007/s10203-022-00374-x

• 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 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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