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Hyperfinite construction of G-expectation
http://hdl.handle.net/10419/111073
Title: Hyperfinite construction of G-expectation
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<br/>Authors: Fadina, Tolulope; Herzberg, Frederik
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<br/>Abstract: We prove a lifting theorem, in the sense of Robinsonian nonstandard analysis, for the G-expectation. Herein, we use an existing discretization theorem for the G-expectation by T. Fadina and F. Herzberg (Bielefeld University, Center for Mathematical Economics in its series Working Papers, 503, (2014)).Convex vNM-stable sets for a semi orthogonal game. Part IV: Large economies: The existence theorem
http://hdl.handle.net/10419/111072
Title: Convex vNM-stable sets for a semi orthogonal game. Part IV: Large economies: The existence theorem
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<br/>Authors: Rosenmüller, Joachim
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<br/>Abstract: Within this paper we establish the existence of a vNM-Stable Set for (cooperative) linear production games with a continuum of players. The coalitional function is generated by r+1 "production factors" (non atomic measures). r factors are given by orthogonal probabilities ("cornered" production factors) establishing the core of the game. Factor r+1 (the "centralized" production factor) is represented by a nonantomic measure with carrier "across the corners" of the market; i.e., this factor is more abundantly available and the representing measure is not located within the core of the game. The present paper continues a series of presentations of this topic, for Part I, II, III, see IMW Working Papers 483, 498 and 500, respectively. We focus on convex vNM-Stable Sets of the game and we present an existence theorem valid for "Large Economies" (the termin is not quite orthodox). There are some basic assumptions for the present model which enable us to come up with a comprehensive version of an existence theorem. However, in order to make our presentation tractable (and readable) we wisely restrict ourselves to a simplified model. As in our previous models there is a (not necessarily unique) imputation outside the core such that the vNM-Stable Set is the convex hull of this imputation and the core. Significantly, this additional imputation can be seen as a truncation of the "centralized" distribution, i.e., the r+1st production factor. Hence there is a remarkable similarity mutatis mutandis regarding the Characterization Theorem that holds true for the "purely orthogonal case."Stock price related financial fragility and growth patterns
http://hdl.handle.net/10419/111071
Title: Stock price related financial fragility and growth patterns
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<br/>Authors: Aßmuth, Pascal
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<br/>Abstract: The total output of an economy usually follows cyclical movements which are accompanied by similar movements in stock prices. The common explanation relies on the demand side. It points out that stock market wealth drives consumption which triggers production afterward. This paper focuses on influences via the supply side of the economy. The aim of the paper is to explore channels where stock price patterns influence the amount of credit taken by firms. We examine trend and volatility cycles at the stock market for their impact on the real economy. For each one we find an application to the investment behaviour of firms. There are three channels addressed: the stock market valuation as piece of information for the assessment of a firm's creditworthiness, the influence on restructuring prospects in times of financial distress and the stock market related remuneration of the top management affecting capital demand. We ask to which extent a channel may contribute to the stock price - output relation when there is mutual feedback. A model à la Delli Gatti et al. (2005) drives the results. Firms take credit to finance their production which determines their financial fragility. If their stochastic revenue is too low, they are bankrupt and leave the economy. The capital loss hurts the bank's equity base and future credit supply is diminished. This causes business cycles. Results show that if the bank assesses creditworthiness according to the stock price then idiosyncratic stock price fluctuations have only a slight effect as they disturb selection and hinder growth. If stock market optimism matters for bankruptcy ruling the level of stock owners' influence does not matter. If optimism is wide spread among stock investors however, investment behaviour is also correlated through the stock prices and this results in huge real economy cycles without any long-term growth. If volatility is considered in the decision of managers they act more prudently and this fosters growth.Dynamic consistent alpha-maxim expected utility
http://hdl.handle.net/10419/111070
Title: Dynamic consistent alpha-maxim expected utility
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<br/>Authors: Beißner, Patrick; Lin, Qian
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<br/>Abstract: We establish a class of fully nonlinear conditional expectations. Similarly to the usage of linear expectations when a probabilistic description of uncertainty is present, we observe analogue quantitative and qualitative properties. The type of nonlinearity captures the agents sentiments of optimism and pessimism in an ambiguous environment. We then introduce an expected utility under a nonlinear expectation, and show monotonicity and continuity of utility. Risk aversion is characterized, and the properties of the certainty equivalent are discussed. Finally, we derive an Arrow-Pratt approximation of the static certainty equivalent and investigate the dynamic version via recursive equations.