Robust pricing--hedging duality for American options in discrete time financial markets

We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we consider an abstract setting, which includes the classical case with a fixed reference probability measure as well as the robust framework with a non-dominated family of probability measures. Our first insight is that by considering a (universal) enlargement of the space, we can see American options as European options and recover the pricing-hedging duality, which may fail in the original formulation. This may be seen as a weak formulation of the original problem. Our second insight is that lack of duality is caused by the lack of dynamic consistency and hence a different enlargement with dynamic consistency is sufficient to recover duality: it is enough to consider (fictitious) extensions of the market in which all the assets are traded dynamically. In the second part of the paper we study two important examples of robust framework: the setup of Bouchard and Nutz (2015) and the martingale optimal transport setup of Beiglb\"ock et al. (2013), and show that our general results apply in both cases and allow us to obtain pricing-hedging duality for American options.Comment: 29 page

On time-consistent equilibrium stopping under aggregation of diverse discount rates

This paper studies the central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with a smooth aggregation preference to incorporate all heterogeneous discount rates with an attitude function that reflects the aggregation rule in the same spirit of ambiguity aversion in the smooth ambiguity preference proposed in Klibanoff et al.(2005). The optimal stopping problem renders to be time inconsistent, for which we develop an iterative approach using consistent planning and characterize all time-consistent equilibria as fixed points of an operator in the setting of one-dimensional diffusion processes. We provide some sufficient conditions on both the underlying models and the attitude function such that the smallest equilibrium attains the optimal equilibrium in which the attitude function becomes equivalent to the linear aggregation rule as of diversity neutral. When the sufficient condition of the attitude function is violated, we can illustrate by various examples that the characterization of the optimal equilibrium may differ significantly from some existing results for an individual agent, which now sensitively depends on the attitude function and the diversity distribution of discount rates

A sparse grid approach to balance sheet risk measurement

In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distribution. For the pricing and hedging model, we chose a classical Black & Scholes model with a stochastic interest rate following a Hull & White model. The risk management model describing the evolution of the parameters of the pricing and hedging model is a Gaussian model. The new numerical method is compared with the traditional nested simulation approach. We review the convergence of both methods to estimate the risk indicators under consideration. Finally, we provide numerical results showing that the sparse grid approach is extremely competitive for models with moderate dimension.Comment: 27 pages, 7 figures. CEMRACS 201

A sparse grid approach to balance sheet risk measurement

In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distribution. For the pricing and hedging model, we chose a classical Black & choles model with a stochastic interest rate following a Hull & White model. The risk management model describing the evolution of the parameters of the pricing and hedging model is a Gaussian model. The new numerical method is compared with the traditional nested simulation approach. We review the convergence of both methods to estimate the risk indicators under consideration. Finally, we provide numerical results showing that the sparse grid approach is extremely competitive for models with moderate dimension

Finance Robuste : une approche de randomisation du modèle

This PhD dissertation presents three research topics. The first two topics are related to the domain of robust finance and the last is related to a numerical method applied in risk management of insurance companies. In the first part, we focus on the problem of super-replication duality for American options in discrete time financial models. We con- sider the robust framework with a family of non-dominated probability measures and the trading strategies are dynamic on the stocks and static on the options. We use two differ- ent ways to obtain the pricing-hedging duality. The first insight is that we can reformulate American options as European options on an enlarged space. The second insight is that by considering a fictitious extensions of the market on which all the assets are traded dynamically. We then show that the general results apply in two important examples of the robust framework. In the second part, we consider the problem of super-replication and utility maximization with proportional transaction cost in discrete time financial market with model uncertainty. Our key technique is to convert the original problem to a frictionless problem on an enlarged space by using a randomization technique to get her with the minimax theorem. For the super-replication problem, we obtain the duality results well-known in the classical dominated context. For the utility maximization problem, we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the third part, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of an insurance company. We compare the new numerical method with the traditional nested simulation approach and review the convergence of both methods to estimate the risk indicators under consideration.Dans cette thèse, on considère trois sujets. Les deux premiers sujets sont liés avec la domaine de robuste finance et le dernier est une méthode numérique appliqué sur la gestion du risque des entreprises d’assurance. Dans la première partie, on considère le problème de la surréplication des options américaines au temps discret. On considère une famille non-dominée des mesures de probabilité et les stratégies de trading sont dynamiques pour les sous-jacents et statiques pour les options. Pour obtenir la dualité de valorisation-couverture, on a deux méthodes. La première méthode est de reformuler les options américaines comme options européens dans un espace élargi. La deuxième méthode est de considérer un marché fictif dans lesquelles stratégies pour tous les actifs sont dynamiques. Ensuite on applique le résultat général à deux exemples importants dans le contexte robuste. Dans la deuxième partie, on considère le problème de sur-réplication and maximisation d’utilité au temps discret avec coût de trans action sous l’incertitude du modèle. L’idée principale est de convertir le problème original à un problème sans friction dans un espace élargi en utilisant un argument de randomisation et le théorème de minimax. Pour le problème de sur-réplication, on obtient la dualité comme dans le cas classique. Pour le problème de maximisation d’utilité, en utilisant un argument de la programmation dynamique, on peut prouver à la fois l’existence de la stratégie optimale et le théorème de la dualité convexe. Dans le troisième partie, on présente une méthode numérique basé sur l’approximation du sparse grid pour calculer la distribution de la perte du bilan d’un entreprise d’assurance. On compare la nouvelle méthode numérique avec l’approche classique de la simulation et étudie la vitesse de la convergence des deux méthodes pour estimer l’indicateur du risque

A low-concentration sulfone electrolyte enables high-voltage chemistry of lithium-ion batteries

Commercial carbonate electrolytes with poor oxidation stability and high flammability limit the operating voltage of Li-ion batteries (LIBs) to ~4.3 V. As one of the most promising candidates for electrolyte solvents, sulfolane (SL) has received significant interest because of its wide electrochemical window, low flammability and high dielectric permittivity. Unfortunately, SL-based electrolytes with normal concentrations cannot achieve highly reversible Li+ intercalation/deintercalation in graphite anodes due to an ineffective solid electrolyte interface, thus undermining their potential application in LIBs. Here, a low-concentration SL-based electrolyte (LSLE) is developed for high-voltage graphite||LiNi0.8Co0.1Mn0.1O2 (NCM811) full cells. A highly reversible graphite anode can be achieved through the preferential decomposition of the dual-salt LiDFOB-LiBF4 in the LSLE. The addition of fluorobenzene further restrains the decomposition of SL, endowing uniform, robust and inorganic-rich interphases on the electrode surfaces. As a result, the LSLE with improved thermal stability can support the MCMB||NCM811 full cells at 4.4 V, evidenced by an excellent cycling performance with capacity retentions of 83% after 500 cycles at 25 ℃ and 82% after 400 cycles at 60 ℃. We believe that the design of this fluorobenzene-containing LSLE offers an effective routine for next-generation low-cost and safe electrolytes for high-voltage LIBs