The 6Th Conference on Mathematical Analysis in Economic Theory

The 6th Conference on Mathematical Analysis in Economic Theory

Date: January 26(Mon)– 29(Thu), 2015 Venue: Lecture Hall, East Research Building, Keio University 2-15-45 Mita, Minato-ku, Tokyo 108-8345, JAPAN organized by The Japanese Society for Mathematical Economics cosponsored by Keio Economic Society, The Oak Society, Inc.

Programme

January 26 (Monday) *Speaker

Morning

Chair: Takuji Arai (Keio University) 9:00–10:00 Keita Owari (The University of Tokyo) On the Lebesgue property and related regularities of monotone convex functions on Orlicz spaces 10:00–11:00 Shigeo Kusuoka (The University of Tokyo) Expectation of diffusion process with absorbing boundary 11:10–12:10 Robert Anderson* (UC Berkeley), L.R. Goldberg, N. Gunther The cost of ﬁnancing leveraged US equity through futures

© Springer Science+Business Media Singapore 2016 181 S. Kusuoka, T. Maruyama (eds.), Advances in Mathematical Economics Volume 20, Advances in Mathematical Economics, DOI 10.1007/978-981-10-0476-6 182 The 6th Conference on Mathematical Analysis in Economic Theory

Afternoon

Chair: Ryozo Miura (Hitotsubashi University) 13:30–14:30 Takuji Arai (Keio University) Local risk-minimization for Barndorff-Nielsen and Shephard models 14:30–15:30 Katsumasa Nishide (Yokohama National University) Heston-type stochastic volatility with a Markov switching regime

Chair: Ken Urai (Osaka University) 16:00–17:00 Hisashi Inaba (The University of Tokyo) Recent developments of the basic reproduction number theory in population dynamics 17:00–18:00 Takashi Suzuki* (Meiji Gakuin University), Nobusumi Sagara Exchange economies with inﬁnitely many commodities and a saturated measure space of consumers January 27 (Tuesday)

Morning

Chair: Takashi Suzuki (Meiji Gakuin University) 9:00–10:00 Yuhki Hosoya (Kanto Gakuin University) The NLL axiom and integrability theory 10:00–11:00 Nobusumi Sagara (Hosei University) An indirect method of nonconvex variational problems in Asplund spaces : the case for saturated measure spaces 11:10–12:10 Ali Khan* (Johns Hopkins University), Yongchao Zhang On pure-strategy equilibria in games with correlated information Afternoon

Chair: Hidetoshi Komiya (Keio University) 13:30–14:30 Hiroyuki Ozaki (Keio University) Upper-convergent dynamic programming 14:30–15:30 Vladimir Tikhomirov (Moscow State University) “Problems of the theory of extremal problems and applications”

Chair: Ali Khan (Johns Hopkins University) 16:00–17:00 Alexander Ioffe (Israel Institute of Technology) On curves of descent 17:00–18:00 Arturo Kohatsu-Higa (Ritsumeikan University) The probabilistic parametrix method as a simulation method (ten- tative) The 6th Conference on Mathematical Analysis in Economic Theory 183

January 28 (Wednesday)

Morning

Chair: Kazuya Kamiya (The University of Tokyo) 9:00–10:00 Yoshiyuki Sekiguchi (Tokyo University of Marine Science and Technology) Real algebraic methods in optimization 10:00–11:00 Ronaldo Carpio (University of International Business & Eco- nomics) Fast Bellman iteration: An application of Legendre-Fenchel dual- ity to inﬁnite-horizon dynamic programming in discrete time 11:10–12:10 Takashi Kamihigashi (Kobe University) Extensions of Fatou’s lemma and the dominated convergence theorem Poster Session

12:10–13:30 Takeshi Ogawa (Hiroshima Shudo University) Intermediate goods with Leontief ’s model and joint production with activity analysis in Ricardian comparative advantage Satoru Kageyama (Osaka University), Ken Urai Fiscal stabilization policy in a Phillips model with unstructured uncertainty Hiromi Murakami (Osaka University), Ken Urai Replica core equivalence theorem: an extension of Debreu-Scarf limit theorem to double inﬁnity monetary economies Ryonfun Im (Kobe University), Takashi Kamihigashi An equilibrium model with two types of asset bubbles Afternoon

Chair: Shinichi Suda (Keio University) 13:30–14:30 Makoto Hanazono (Nagoya University) Procurement auctions with general price-quality evaluation 14:30–15:30 Chiaki Hara* (Kyoto University), Kenjiro Hirata Dynamic inconsistency in pension fund management

Chair: Shigeo Kusuoka (The University of Tokyo) 16:00–17:00 Chia-Hui Chen (Kyoto University) A tenure-clock problem: evaluation, deadline, and up-or-out 17:00–18:00 Nozomu Muto* (Yokohama National University), Shin Sato Bounded response and Arrow’s impossibility

18:30–21:00 Reception at Tsunamachi Mitsui Club 184 The 6th Conference on Mathematical Analysis in Economic Theory

January 29 (Thursday) Satellite Session

Morning

Chair: Hiroyuki Ozaki (Keio University) 9:00–9:30 Masayuki Yao (Keio University) Recursive utility and dynamic programming under the assumption of upper convergence: an order-theoretic approach 9:30–10:00 Chaowen Yu (Keio University) Locally robust mechanism design 10:00–10:30 Hiromi Murakami* (Osaka University), Ken Urai Replica core equivalence theorem: an extension of Debreu-Scarf limit theorem to double inﬁnity monetary economies 11:00–11:30 Kohei Shiozawa* (Osaka University), Ken Urai A generalization of social coalitional equilibrium for multiple coalition structures 11:30–12:00 Takeshi Ogawa (Hiroshima Shudo University) Intermediate goods with Leontief ’s model and joint production with activity analysis in Ricardian comparative advantage

Robert Anderson Takashi Suzuki

Yuhki Hosoya Nobusumi Sagara The 6th Conference on Mathematical Analysis in Economic Theory 185

Ali Khan Chiaki Hara

Vladimir Tikhomirov, Toru Maruyama, Alexander Ioffe 186 The 6th Conference on Mathematical Analysis in Economic Theory

Saying “Good-bye" at the reception (Tsunamachi Mitsui Club) Index

A Commodity characteristics, 105 Absolute moment of the second order, 154 Compact metric space, 105 Adjunction’method, 163 Construction of ﬁelds, 145–146 Almost periodic, 162 Core, 105 weakly stationary process, 162 Covariance, 154 Archimedean, 93 Cramér-Kolmogorov theorem, 160 Aumann-Bochner fractional, 57 Aumann integral, 35 Aumann-Pettis fractional, 56 D Aumann’s equivalence theorem, 105 Demand function, 86 Dierentiated commodities, 105 Differentiability, 132 Dirac measures, 108 B Distributionalized formulation, 106 Barndorff-Nielsen and Shephard models, 3–21 Doob-Kawata formulas, 160 Behavioral strategy, 113 Bochner-integrable function, 33 E mappings, 25 Eberlein-Smulian theorem, 35, 44 Bochner theorem, 157–158 "-almost period, 161 Bolza problem, 137 Euler equation, 137 Boundary value problem, 24 Existence in calculus of variations, 147–148 ˛;1Œ0; 1/ WB;E -solution to the, 43 Expectation, 154 Bounded marginal rate of substitution, 106 Expenditure function, 86

C F Carathéodory Fatou’s lemma, 107 integrand, 70 Finite convergence property, 94 mapping, 52 Finite orthogonal measure, 159 Cardinality of the set of agents, 111 Föllmer-Schweizer decomposition, 11 Carleson theorem, 164 Fourier transform (resp.inverse Fourier Character group/daul group, 156 transform), in the sense of Coalitional formulation, 106 Planchere, 171

© Springer Science+Business Media Singapore 2016 187 S. Kusuoka, T. Maruyama (eds.), Advances in Mathematical Economics Volume 20, Advances in Mathematical Economics, DOI 10.1007/978-981-10-0476-6 188 Index

Fractional bochner integral, 25–28 Lasserre’s hierarchy, 93 Fractional differential equation (FDE), 24, 67 Lebesgue-measurable, 29 solutions set .(SZ /,68 Lemma on non triviality of annihilator, 135 ˛;1 .Œ0; 1/ WB;E solutions set to the, 33, 39, 68, Level sets, 61 71, 72 Leverage effect, 4 Fractional differential inclusion (FDI), 24, Locally compact commutative topological 33–38, 65 group, 156 ˛;1 .Œ0; 1/ WB;E solutions set to the, 33, 39, 41, Lotteries, 112 45, 47 Lyapunov’s theorem, 107 Fractional fuzzy differential inclusion, 61–63 Fractional Pettis integral, 28–33 Fractional w-R.L derivative of order, 24, 25, M 30, 38 Mackey topology, 30, 37, 46, 51 Free Abelian group, 107 Malliavin calculus, 13 Fundamental bifurcation, 113 Measurable selections, 52 Minimal martingale measure (MMM), 5 Moment problem, 93 G Monopoly power, 104 Gamma function, 28 Moving average process, 156 Gamma-OU, 6 Multivalued Aumann-Pettis integral, 57 Gelfand integration, 107 Multivalued fractional Aumann-Pettis integral, Global solution, 78 57 Multivalued fractional Pettis integral, 56–67 inclusion, 52 H Multivalued Pettis integral inclusion, 52, 54 Herglotz Theorem, 156–157 Household economics, 105 N Narrow topology, 67 I Nonextendable solution, 79 Ideal, 92 Nonnegative orthant, 78 IG-OU, 6 Nonstandard analysis, 113 Imperfect competition, 104 Individualistic formulation, 106 O Individualized economy, 116 Optimal control problem, 144–145 Infinitesimal amounts, 105 Ordinary dierential equation (ODE), 24 Inner product, 91 Ornstein-Uhlenbeck process, 4 Integrable, 79 Orthogonal measure, 159 selections, 36 Integrably bounded mapping, 61 P multifunction, 43 Partial differential equation, 77–87 multimapping, 58 Periodic weakly stationary process, 160 Pettis-integrable, 28 functions, 28, 38 K mapping, 30 Kakutani-Ky Fan fixed point theorem, 37, 51, Pettis norm, 28 56, 60 Polynomial optimization problems, 90 Positive orthant, 78 Positive semi-definite, 156 L Lagrange problem of calculus of variations, 142 Q Large economy, 105 Quadratic module, 92 Index 189

R Symmetrization, 114 Randomized choice, 113 System of ﬁnite dimensional distributions, 154 Real radical, 92 Registers, 113 Relatively weakly compact, 33 T Riemann-Liouville fractional derivative, 25 .E; E/,37 Right-inverse mapping theorem, 133–134 Topology, 175 of pointwise convergence on L1 ˝ E 39, 40 of uniform convergence, 45 S Trigonometric polynomial, 179 Saturated economy, 116 Truncated ideal, 92 Saturated (super-atomless) measure space, 107 Truncated quadratic module, 92 saturated measure spaces (Homogeneous), 115 Scalarly integrable function, 28 Scalarly sequentially upper semicontinuous, U 36, 60 Uniformly good substitutes, 110 Scalarly uniformly integrable, 28–29 Uniformly integrable, 28 Scalarly upper semicontinuous, 58 Upper hemi-continuous, 116 . 1 ; 1/ LE LE -compact set, 45 Utility function, 86 . 1 ; 1 ˝ / PE L E -convergence, 40 Second order ordinary dierential equation (SODE), 24 V Semialgebraic set, 90 Vanishing ideal, 92 Semideﬁnite programming problem, 91 Variance, 155 Separability, 133 Variety, 92 Serially uncorrelatedness, 156 Volatility risk premium, 4 Slutsky process, 152 Smooth-convex Lagrange principle, 140–142 Smooth problems, 142–143 W Space of signed measures, 105 Walrasian general equilibrium theory, 104 Spectral density function, 158 Walras’ law, 84 Spectral measure, 158 Weakly compact, 36 Stable topology, 67, 72 Stochastic volatility, 4 Strassen theorem, 57 Y Sum of square polynomials (SOS), 91 Young measures, 24, 67, 68, 72 relaxation, 93 control, 67, 68