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A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.



Law of large numbers and Ergodic Theorem for convex weak star compact valued Gelfand-integrable mappings

We prove several results in the integration of convex weak star (resp. norm compact) valued random sets with application to weak star Kuratowski convergence in the law of large numbers for convex norm compact valued Gelfand-integrable mappings in the dual of a separable Banach space. We also establish several weak star Kuratowski convergence in the law of large numbers and ergodic theorem involving the subdifferential operators of Lipschitzean functions defined on a separable Banach space, and also provide an application to a closure type result arisen in evolution inclusions.
C. Castaing, P. Raynaud de Fitte

Discounted optimal growth in a two-sector RSS model: a further geometric investigation

The geometric apparatus of Khan–Mitra (Adv. Math. Econ. 8:349–381, 2006; Jpn. Econ. Rev. 58:191–225, 2007) enables an identification of a tripartite (inside-borderline-outside) distinction for discounted Ramseyian optimality in the 2-sector RSS model and to obtain the following results: (a) parametric ranges of the discount factor for which the check-map is the optimal policy function, (b) necessary and sufficient conditions for the existence of stable optimal 2-period cycles, (c) absence of 3-period cycles in the borderline case, and (d) existence of unstable 3-period cycles in a canonical instance of the outside case. The geometry is shown to have more general interest and relevance for future work.
M. Ali Khan, Tapan Mitra

Gaussian K-scheme: justification for KLNV method

We give a mathematical justification for the KLNV-method, K-scheme based on Gaussian random variables given in Ninomiya–Victoir (Appl. Math. Financ. 15:107–121, 2008) and Ninomiya–Ninomiya (Finance Stoch. 13:415–443, 2009), by using the partial Malliavin calculus and Lie algebra.
Shigeo Kusuoka

Competitive equilibria of a large exchange economy on the commodity space ℓ∞

The existence of competitive equilibrium for a large exchange economy over the commodity space will be discussed. We define the economy as a distribution on the space of consumers’ characteristics following Hart and Kohlberg (J. Math. Econ. 1:167–174, 1974), and prove the theorem without the assumption of convexity of preferences.
Takashi Suzuki

Local consistency of the iterative least-squares estimator for the semiparametric binary choice model

Wang and Zhou propose an iterative estimation algorithm for the binary choice model in “Working paper no. E-180-95, the Center for Business and Economic Research, College of Business and Economics, University of Kentucky (1995).” The method is easy-to-implement, semiparametric, and free from choosing nonparametric tuning parameters such as a kernel bandwidth. In this paper, a rigorous proof for consistency of the estimator will be given.
Hisatoshi Tanaka


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