Equivalence of axioms for bankruptcy problems

The bankruptcy problem is concerned with how to divide the net worth of the bankrupt firm among its creditors. In this paper, we investigate the logical relations between various axioms in the context of bankruptcy. Those axioms are: population-and-resource monotonicity, consistency, converse consistency, agreement, and separability. In most axiomatic models, they are not directly related. However, we show that they are equivalent on the class of bankruptcy problems under minor additional requirements. Received: April 1998/Revised version: January 1999     

Game theoretic analysis of negotiations under bankruptcy

We extend the contingent claims framework for the levered firm in explicitly modelling the resolution of financial distress under formal bankruptcy as a non-cooperative game between claimants under the supervision of the bankruptcy judge. The identity of the class of claimants proposing the first reorganization plan is found to be a key determinant of the time spent under bankruptcy, the likelihood of liquidation and the renegotiated value of claims. Our quantitative results confirm the economic intuition that a bankruptcy design must trade-off the initial priority of claims with the viability of reorganized firms.     

A coalitional procedure leading to a family of bankruptcy rules

We provide a general coalitional procedure that characterizes a family of rules for bankruptcy problems inspired by the Talmud.     

Mean-risk portfolio management with bankruptcy prohibition

In accordance with Solvency II, the commonly tightened government regulation on insurance cooperations, they have been obligated to take conservative investment strategies such as those ruling out the possibility of bankruptcy. With this in mind, in this article, we aim to continue our work (Wong et al., 2017a,b) . First, we study the solvability of mean-risk portfolio optimization problem with bankruptcy prohibition, in the complete market in which the investor aims to maximize the expected payoff and to minimize the deviation risk simultaneously, which is of great use in the insurance paradigm. Secondly, we also provide the original weak convergence result of the optimal terminal wealth of a sequence of approximate markets to that of the limiting market through their corresponding pricing kernels. As a result, we establish an effective numerical algorithm calibrating the optimal terminal wealth under Black–Scholes models by that of binomial tree models. The results of our numerical simulations indicate that the downside risk of the optimal payoff can be effectively reduced by imposing the bankruptcy prohibition.     

Weighted bankruptcy rules and the museum pass problem

In this paper we introduce and characterize some allocation rules for weighted bankruptcy problems. We illustrate the relevancy of weighted bankruptcy by applying it to analyse the museum pass problem, introduced by Ginsburgh and Zang (2003). This application is completed with the analysis of real data for the “Card Musei” of the Municipality of Genova.     

DEA as a tool for bankruptcy assessment: A comparative study with logistic regression technique

This paper proposes data envelopment analysis (DEA) as a quick-and-easy tool for assessing corporate bankruptcy. DEA is a non-parametric method that measures weight estimates (not parameter estimates) of a classification function for separating default and non-default firms. Using a recent sample of large corporate failures in the United States, we examine the capability of DEA in assessing corporate bankruptcy by comparing it with logistic regression (LR). We find that DEA outperforms LR in evaluating bankruptcy out-of-sample. This feature of DEA is appealing and has practical relevance for investors. Another advantage of DEA over LR is that it does not have assumptions associated with statistical and econometric methods. Furthermore, DEA does not need a large sample size for bankruptcy evaluation, usually required by such statistical and econometric approaches. The need for such a large sample size is a significant disadvantage to practitioners when investment decisions are made using small samples. DEA can bypass such a difficulty related to a sample size. Thus, DEA is a practically appealing method for bankruptcy assessment.     

Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties

The Reverse Talmud rule for bankruptcy problems applies the Constrained Equal Awards rule (CEA rule) for ‘large’ amounts of the estate, while it applies the Constrained Equal Losses rule (CEL rule) for ‘small’ amounts of the estate. The CEA rule, respectively CEL rule, can be axiomatized using the Exemption and Exclusion properties respectively. There is no rule that satisfies both these two properties. In this paper we axiomatize the Reverse Talmud rule by using compatible weaker versions of the Exemption and Exclusion properties.     

Using Bayesian networks for bankruptcy prediction: Some methodological issues

This study provides operational guidance for building naïve Bayes Bayesian network (BN) models for bankruptcy prediction. First, we suggest a heuristic method that guides the selection of bankruptcy predictors. Based on the correlations and partial correlations among variables, the method aims at eliminating redundant and less relevant variables. A naïve Bayes model is developed using the proposed heuristic method and is found to perform well based on a 10-fold validation analysis. The developed naïve Bayes model consists of eight first-order variables, six of which are continuous. We also provide guidance on building a cascaded model by selecting second-order variables to compensate for missing values of first-order variables. Second, we analyze whether the number of states into which the six continuous variables are discretized has an impact on the model’s performance. Our results show that the model’s performance is the best when the number of states for discretization is either two or three. Starting from four states, the performance starts to deteriorate, probably due to over-fitting. Finally, we experiment whether modeling continuous variables with continuous distributions instead of discretizing them can improve the model’s performance. Our finding suggests that this is not true. One possible reason is that continuous distributions tested by the study do not represent well the underlying distributions of empirical data. Finally, the results of this study could also be applicable to business decision-making contexts other than bankruptcy prediction.     

Optimal dividends and bankruptcy procedures: Analysis of the Ornstein-Uhlenbeck process

This paper investigates the impact of bankruptcy procedures on optimal dividend barrier policies. We specifically focus on Chapter 11 of the US Bankruptcy Code, which allows a firm in default to continue its business for a certain period of time. Our model is based on the surplus of a firm that earns investment income at a constant rate of credit interest when it is in a creditworthy condition. The firm pays a debit interest rate that depends on the deficit level when it is in financial distress. Thus, the surplus follows an Ornstein-Uhlenbeck (OU) process with a negative surplus-dependent mean-reverting rate. Default and liquidation are modeled as distinguishable events by using an excursion time or occupation time framework. This paper demonstrates how the optimal dividend barrier can be obtained by deriving a closed-form solution for the dividend value function. It also characterizes the distributional property and expectation of bankruptcy time subject to the bankruptcy procedure. Our numerical examples show that under an optimal dividend barrier strategy, the bankruptcy procedure may not prolong the expected bankruptcy time in some situations.     

Duality in land rental problems

Land rental problems describe situations where one tenant demands land from several lessors. The way lessors rent their land can be seen as equivalent to a bankruptcy problem. We extend the idea of self-duality in bankruptcy problems to land rental problems. We provide a complete characterization of the family of rules that satisfy self-duality. Moreover, self-duality is enough to assure the proportional land share among lessors. Adding other reasonable properties, we pick up a single rule.     

A result in surrogate duality for certain integer programming problems

We consider linear programming problems with some equality constraints. For such problems, surrogate relaxation formulations relaxing equality constraints existwith zero primal-dual gap both when all variables are restricted to be integers and when no variable is required to be integer. However, for such surrogate formulations, when the variables are mixed-integer, the primal-dual gap may not be zero. We establish this latter result by a counterexample.     

The equal award principle in problems with constraints and claims

In this paper we study how, under the equal award principle, to distribute a resource among different agents with a claim on it, when there are some constraints in the problem. Some properties of the rule are given as well as an axiomatic characterisation.     

Integer solutions to bankruptcy problems with non-integer claims

In this paper, we consider a bankruptcy problem with the additional constraint that the estate has to be assigned in integer unities; differently from the approaches by other authors, we allow for non-integer claims. This situation poses new questions on the existence and the uniqueness of the solution. We propose a new solution method that leads to the “box solution”, for which uniqueness may be guaranteed introducing a ranking on the claimants. Some examples complete the paper.     

Conjugate dual problems in constrained set-valued optimization and applications

In this paper, two conjugate dual problems are proposed by considering the different perturbations to a set-valued vector optimization problem with explicit constraints. The weak duality, inclusion relations between the image sets of dual problems, strong duality and stability criteria are investigated. Some applications to so-called variational principles for a generalized vector equilibrium problem are shown.     

Conjugate duality for vector-maximization problems

In this article we present a conjugate duality for a problem of maximizing a polyhedral concave nondecreasing homogeneous function over a convex feasible set in the nonnegative n-dimensional orthant. Using this duality we obtain a zero-gap duality for a vector-maximization problem.     

Conjugate duality for multiobjective composed optimization problems

Given a multiobjective optimization problem with the components of the objective function as well as the constraint functions being composed convex functions, we introduce, by using the Fenchel-Moreau conjugate of the functions involved, a suitable dual problem. Under a standard constraint qualification and some convexity as well as monotonicity conditions we prove the existence of strong duality. Finally, some particular cases of this problem are presented.      

Computation of the random arrival rule for bankruptcy problems

Bankruptcy problems are a fundamental class of fair division problems in microeconomics. Among the various solution concepts proposed for the problem, the random arrival rule is one of the most prominent. In this paper, we conduct a computational analysis of the rule. It is shown that the allocation returned by the rule is #P-complete to compute. The general complexity result is complemented by a pseudo-polynomial-time dynamic programming algorithm for the random arrival rule.     

一类非光滑规划问题的最优性和对偶

研究一类非光滑多目标规划问题,给出了该规划问题的三个最优性充分条件.同时,研究了该问题的对偶问题,给出了相应的弱对偶定理和强对偶定理.     

On the relationship between fenchel and Lagrange duality for optimization problems in general spaces

In this paper, the equivalence between a Fenchel and Lagrange duality theorem for optimization problems in dual pairs of real vector spaces is proved in a direct way.