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Register a new userOn incompleteness of bond markets with infinite number of random factors
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The completeness of a bond market model with infinite number of sources of randomness on a finite time interval in the Heath-Jarrow-Morton framework is studied. It is proved that the market is not complete. A construction of a bounded contingent claim, which can not be replicated, is provided.
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These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.
The dynamics of financial markets are driven by the interactions between participants, as well as the trading mechanisms and regulatory frameworks that govern these interactions. Decision-makers would rather not ignore the impact of other participants on these dynamics and should employ tools and models that take this into account. To this end, we demonstrate the efficacy of applying opponent-modeling in a number of simulated market settings. While our simulations are simplified representations of actual market dynamics, they provide an idealized playground in which our techniques can be demonstrated and tested. We present this work with the aim that our techniques could be refined and, with some effort, scaled up to the full complexity of real-world market scenarios. We hope that the results presented encourage practitioners to adopt opponent-modeling methods and apply them online systems, in order to enable not only reactive but also proactive decisions to be made.
We adress the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where the price process of risky assets can have a default time. Using dynamic programming, we characterize the value function with a backward stochastic differential equation and the optimal portfolio policies. We separately treat the cases of exponential, power and logarithmic utility.
We prove that the number of Hamilton cycles in the random graph G(n,p) is n!p^n(1+o(1))^n a.a.s., provided that pgeq (ln n+ln ln n+omega(1))/n. Furthermore, we prove the hitting-time version of this statement, showing that in the random graph process, the edge that creates a graph of minimum degree 2 creates (ln n/e)^n(1+o(1))^n Hamilton cycles a.a.s.
We formulate an equilibrium model of intraday trading in electricity markets. Agents face balancing constraints between their customers consumption plus intraday sales and their production plus intraday purchases. They have continuously updated forecast of their customers consumption at maturity with decreasing volatility error. Forecasts are prone to idiosyncratic noise as well as common noise (weather). Agents production capacities are subject to independent random outages, which are each modelled by a Markov chain. The equilibrium price is defined as the price that minimises trading cost plus imbalance cost of each agent and satisfies the usual market clearing condition. Existence and uniqueness of the equilibrium are proved, and we show that the equilibrium price and the optimal trading strategies are martingales. The main economic insights are the following. (i) When there is no uncertainty on generation, it is shown that the market price is a convex combination of forecasted marginal cost of each agent, with deterministic weights. Furthermore, the equilibrium market price follows Almgren and Chrisss model and we identify the fundamental part as well as the permanent market impact. It turns out that heterogeneity across agents is a necessary condition for the Samuelsons effect to hold. (ii) When there is production uncertainty, the price volatility becomes stochastic but converges to the case without production uncertainty when the number of agents increases to infinity. Further, on a two-agent case, we show that the potential outages of a low marginal cost producer reduces her sales position.
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