Investment under uncertainty, competition and regulation

We investigate a randomization procedure undertaken in real option games which can serve as a basic model of regulation in a duopoly model of preemptive investment. We recall the rigorous framework of [M. Grasselli, V. Lecl\`ere and M. Ludkovsky, Priority Option: the value of being a leader, International Journal of Theoretical and Applied Finance, 16, 2013], and extend it to a random regulator. This model generalizes and unifies the different competitive frameworks proposed in the literature, and creates a new one similar to a Stackelberg leadership. We fully characterize strategic interactions in the several situations following from the parametrization of the regulator. Finally, we study the effect of the coordination game and uncertainty of outcome when agents are risk-averse, providing new intuitions for the standard case

Uniform rationality of Poincar\'e series of p-adic equivalence relations and Igusa's conjecture on exponential sums

This thesis contains some new results on the uniform rationality of Poincar\'e series of p-adic equivalence relations and Igusa's conjecture on exponential sumsComment: Doctoral thesis, University of Lill

Advanced Capsule Networks via Context Awareness

Capsule Networks (CN) offer new architectures for Deep Learning (DL) community. Though its effectiveness has been demonstrated in MNIST and smallNORB datasets, the networks still face challenges in other datasets for images with distinct contexts. In this research, we improve the design of CN (Vector version) namely we expand more Pooling layers to filter image backgrounds and increase Reconstruction layers to make better image restoration. Additionally, we perform experiments to compare accuracy and speed of CN versus DL models. In DL models, we utilize Inception V3 and DenseNet V201 for powerful computers besides NASNet, MobileNet V1 and MobileNet V2 for small and embedded devices. We evaluate our models on a fingerspelling alphabet dataset from American Sign Language (ASL). The results show that CNs perform comparably to DL models while dramatically reducing training time. We also make a demonstration and give a link for the purpose of illustration.Comment: 12 page

Hedging Expected Losses on Derivatives in Electricity Futures Markets

We investigate the problem of pricing and hedging derivatives of Electricity Futures contract when the underlying asset is not available. We propose to use a cross hedging strategy based on the Futures contract covering the larger delivery period. A quick overview of market data shows a basis risk for this market incompleteness. For that purpose we formulate the pricing problem in a stochastic target form along the lines of Bouchard and al. (2008), with a moment loss function. Following the same techniques as in the latter, we avoid to demonstrate the uniqueness of the value function by comparison arguments and explore convex duality methods to provide a semi-explicit solution to the problem. We then propose numerical results to support the new hedging strategy and compare our method to the Black-Scholes naive approach