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Chebbi S.,King Saud University | Soner H.M.,ETH Zurich | Soner H.M.,Swiss Finance Institute
Nonlinear Analysis: Real World Applications | Year: 2013

We study the classical optimal investment and consumption problem of Merton in a discrete time model with frictions. Market friction causes the investor to lose wealth due to trading. This loss is modeled through a nonlinear penalty function of the portfolio adjustment. The classical transaction cost and the liquidity models are included in this abstract formulation. The investor maximizes her utility derived from consumption and the final portfolio position. The utility is modeled as the expected value of the discounted sum of the utilities from each step. At the final time, the stock positions are liquidated and a utility is obtained from the resulting cash value. The controls are the investment and the consumption decisions at each time. The utility function is maximized over all controls that keep the after liquidation value of the portfolio non-negative. A dynamic programming principle is proved and the value function is characterized as its unique solution with appropriate initial data. Optimal investment and consumption strategies are constructed as well. © 2012 Published by Elsevier Ltd. Source


Sornette D.,ETH Zurich | Sornette D.,Swiss Finance Institute
Reports on Progress in Physics | Year: 2014

This short review presents a selected history of the mutual fertilization between physics and economics - from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the 'Emerging Intelligence Market Hypothesis' to reconcile the pervasive presence of 'noise traders' with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets. © 2014 IOP Publishing Ltd. Source


Saichev A.,ETH Zurich | Saichev A.,Novgorod State University | Sornette D.,ETH Zurich | Sornette D.,Swiss Finance Institute
International Journal of Modern Physics C | Year: 2014

We present a novel simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us to explain both qualitatively and quantitatively important stylized facts observed in the statistics of both microstructure and macrostructure returns, including the short-ranged correlation of returns, the long-ranged correlations of absolute returns, the microstructure noise and Epps effects. According to the microstructure noise effect, volatility is a decreasing function of the time-scale used to estimate it. The Epps effect states that cross correlations between asset returns are increasing functions of the time-scale at which the returns are estimated. The microstructure noise is explained as the result of the negative return correlations inherent in the definition of the bid-ask bounce component (ii). In the presence of a genuine correlation between the returns of two assets, the Epps effect is due to an average statistical overlap of the momentum of the returns of the two assets defined over a finite time-scale in the presence of the long memory process (i). © World Scientific Publishing Company. Source


Yukalov V.I.,ETH Zurich | Yukalov V.I.,Joint Institute for Nuclear Research | Sornette D.,ETH Zurich | Sornette D.,Swiss Finance Institute
IEEE Transactions on Systems, Man, and Cybernetics: Systems | Year: 2014

We investigate how the choice of decision makers can be varied under the presence of risk and uncertainty. Our analysis is based on the approach we have previously applied to individual decision makers, which we now generalize to the case of decision makers that are members of a society. The approach employs the mathematical techniques that are common in quantum theory, justifying our naming as quantum decision theory. However, we do not assume that decision makers are quantum objects. The techniques of quantum theory are needed only for defining the prospect probabilities taking into account such hidden variables as behavioral biases and other subconscious feelings. The approach describes an agent's choice as a probabilistic event occurring with a probability that is the sum of a utility factor and of an attraction factor. The attraction factor embodies subjective and unconscious dimensions in the mind of the decision maker. We show that the typical aggregate amplitude of the attraction factor is 1/4, and it can be either positive or negative depending on the relative attraction of the competing choices. The most efficient way of varying the decision makers choice is realized by influencing the attraction factor. This can be done in two ways. One method is to arrange in a special manner the payoff weights, which induces the required changes of the values of attraction factors. We show that a slight variation of the payoff weights can invert the sign of the attraction factors and reverse the decision preferences, even when the prospect utilities remain unchanged. The second method of influencing the decision makers choice is by providing information to decision makers. The methods of influencing decision making are illustrated by several experiments, whose outcomes are compared quantitatively with the predictions of our approach. © 2013 IEEE. Source


De Treville S.,University of Lausanne | Bicer I.,University of Lausanne | Chavez-Demoulin V.,University of Lausanne | Hagspiel V.,University of Lausanne | And 4 more authors.
Journal of Operations Management | Year: 2014

When do short lead times warrant a cost premium? Decision makers generally agree that short lead times enhance competitiveness, but have struggled to quantify their benefits. Blackburn (2012) argued that the marginal value of time is low when demand is predictable and salvage values are high. de Treville et al. (2014) used real-options theory to quantify the relationship between mismatch cost and demand volatility, demonstrating that the marginal value of time increases with demand volatility, and with the volatility of demand volatility. We use the de Treville et al. model to explore the marginal value of time in three industrial supply chains facing relatively low demand volatility, extending the model to incorporate factors such as tender-loss risk, demand clustering in an order-up-to model, and use of a target fill rate that exceeded the newsvendor profit-maximizing order quantity. Each of these factors substantially increases the marginal value of time. In all of the companies under study, managers had underestimated the mismatch costs arising from lead time, so had underinvested in cutting lead times. © 2014 Elsevier B.V. Source

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