EYRAUD LOISEL Anne

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The aim of this work is to show that incompleteness is due in general not only to a lack of assets, but also to a lack of information. In this paper we present a simple inuence model where the inuencial agent has access to additional information. This leads to the construction of two models, a complete model and an incomplete model where the only dierence is a dierence of information. This leads to a simple model of incomplete market where the number of assets is not the cause of incompleteness: incomplete information is the explanation. Keywords Information · asymmetric information · option pricing · martin-gales · insider trading · complete market · incomplete market AMS Classication (2000): 60H10, 60G44, 60H07, 60J75, 91G20, 91B70, 93E11. JEL Classication: C60,G11,G14.

Pension funds that handle retirement risk need to invest assets in a diversified manner, on long durations and if possible while facing interest rate and longevity risk. In the recent years, a new class of investment called a longevity megafund was described, that invests in clinical trials for solutions against age-related diseases. Using simple models, we here study the financial interest for pension funds of investing in a longevity megafund.

The aim of this work is to show that incompleteness is due in general not only to a lack of assets, but also to a lack of information. In this paper we present a simple inuence model where the inuencial agent has access to additional information. This leads to the construction of two models, a complete model and an incomplete model where the only dierence is a dierence of information. This leads to a simple model of incomplete market where the number of assets is not the cause of incompleteness: incomplete information is the explanation. Keywords Information · asymmetric information · option pricing · martin-gales · insider trading · complete market · incomplete market AMS Classication (2000): 60H10, 60G44, 60H07, 60J75, 91G20, 91B70, 93E11. JEL Classication: C60,G11,G14.

Pension funds that handle retirement risk need to invest assets in a diversified manner, on long durations and if possible while facing interest rate and longevity risk. In the recent years, a new class of investment called a longevity megafund was described, that invests in clinical trials for solutions against age-related diseases. Using simple models, we here study the financial interest for pension funds of investing in a longevity megafund.

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We consider the problem of how to optimally close a large assetposition in a market with a linear temporary price impact. We take the perspectiveof an agent who obtains a signal about the future price evolvement.By means of classical stochastic control we derive explicit formulas for the closingstrategy that minimizes the expected execution costs. We compare agentsobserving the signal with agents who do not see it. We compute explicitly theexpected additional gain due to the signal, and perform a comparative staticsanalysis.

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We consider the problem of how to optimally close a large asset position in a market with a linear temporary price impact. We take the perspective of an agent who obtains a signal about the future price evolvement. By means of classical stochastic control we derive explicit formulas for the closing strategy that minimizes the expected execution costs. We compare agents observing the signal with agents who do not see it. We compute explicitly the expected additional gain due to the signal, and perform a comparative statics analysis.

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In this paper a model with an influent and informed investor is presented. The studied problem is the point of view of a non informed agent hedging an option in this influenced and informed market. Her lack of information makes the market incomplete to the non informed agent. The obtained results, by means of Malliavin calculus and Clark-Ocone Formula, as well as Filtering Theory are the expressions and a comparison between the strategy of the non informed trader, and the strategy of the informed agent. An expression of the residual risk a non informed trader keeps by detaining an option in this influenced and informed market is derived using a quadratic approach of hedging in incomplete market. Finally, the analysis leads to a measure of the lack of information that makes the incompleteness of the market. The financial interpretation is explained throughout the theoretical analysis, together with an example of such influenced informed model.

We study a new risk measure inspired from risk theory with a heat wave risk analysis motivation. We show that this risk measure and its sensitivities can be computed in practice for relevant temperature stochastic processes. This is in particular useful for measuring the potential impact of climate change on heat wave risk. Numerical illustrations are given.

The objective of this thesis is to study the existence and uniqueness of solution of backward stochastic differential equations with filtration magnification. The motivation for this mathematical problem comes from the solution of a financial hedging problem by an agent with unknown additional market information. In a first part, we solve this problem, successively in a continuous framework and then with jumps, and show that under the assumption (H3) of the filtration magnification, thanks to a representation theorem of martingales, the RHSD in the coarse space under standard assumptions has a unique solution. One of the main consequences is that, in a complete market, the possession of additional information by the insider does not give him a different hedging strategy. In a second part, we develop a model of an informed and influential agent, which leads us to solve a backward stepwise stochastic differential equation with filtration magnification, and we also obtain an existence and uniqueness theorem for the solution. We also study the incomplete market hedging problem, since due to the influence, the market without information becomes incomplete. Finally, in the last part, we generalize the existence and uniqueness results of the solution of EDSR with filtration magnification to EDSR with random horizon.

The objective of this thesis is to study the existence and uniqueness of solution of backward stochastic differential equations with filtration magnification. The motivation for this mathematical problem comes from the solution of a financial hedging problem by an agent with unknown additional market information. In a first part, we solve this problem, successively in a continuous framework and then with jumps, and show that under the assumption (H3) of the filtration magnification, thanks to a representation theorem of martingales, the RHSD in the coarse space under standard assumptions has a unique solution. One of the main consequences is that, in a complete market, the possession of additional information by the insider does not give him a different hedging strategy. In a second part, we develop a model of an informed and influential agent, which leads us to solve a backward stepwise stochastic differential equation with filtration magnification, and we also obtain an existence and uniqueness theorem for the solution. We also study the incomplete market hedging problem, since due to the influence, the market without information becomes incomplete. Finally, in the last part, we generalize the existence and uniqueness results of the solution of EDSR with filtration magnification to EDSR with random horizon.