Practitioners sometimes suggest to use a combination of Sobol sequences and orthonormal polynomials when applying an LSMC algorithm for evaluation of option prices or in the context of risk capital calculation under the Solvency II regime. In this paper, we give a theoretical justification why good implementations of an LSMC algorithm should indeed combine these two features in order to assure numerical stability. Moreover, an explicit bound for the number of outer scenarios necessary to guarantee a prescribed degree of numerical stability is derived. We embed our observations into a coherent presentation of the theoretical background of LSMC in the insurance setting.

We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the difference between assets and liabilities of the bank. A bank is solvent when its capital reserves are greater or equal to zero otherwise the bank is failed.The banking system dynamics is defined by an initial value problem for a system of stochastic differential equations whose independent variable is time and whose dependent variables are the assets and the liabilities of the banks.The banking system model presented generalizes those discussed in [4],[3] and describes a homogeneous population of banks. The main features of the model are a cooperation mechanism among banks and the possibility of the (direct) intervention of the monetary authority in the banking system dynamics. We call systemic risk or systemic event in a bounded time interval the fact that in that time interval at least a given fraction of the banks fails. The probability of systemic risk in a bounded time interval is evaluated using statistical simulation. The systemic risk governance pursues the goal of keeping the probability of systemic risk in a bounded time interval between two given thresholds.The monetary authority is responsible for the systemic risk governance.The governance consists in the choice of the assets and of the liabilities of a kind of "ideal bank" as functions of time and in the choice of the rules that regulate the cooperation mechanism among banks.These rules are obtained solving an optimal control problem for the pseudo mean field approximation of the banking system model. The governance induces the banks of the system to behave like the "ideal bank". Shocks acting on the assets or on the liabilities of the banks are simulated.

We propose a robust implementation of the Nerlove--Arrow model using a Bayesian structural time series model to explain the relationship between advertising expenditures of a country-wide fast-food franchise network with its weekly sales. Thanks to the flexibility and modularity of the model, it is well suited to generalization to other markets or situations. Its Bayesian nature facilitates incorporating \emph{a priori} information (the manager's views), which can be updated with relevant data. This aspect of the model will be used to present a strategy of budget scheduling across time and channels.

I study optimal disclosure policies in sequential contests. A contest designer chooses at which periods to publicly disclose the efforts of previous contestants. I provide results for a wide range of possible objectives for the contest designer. While different objectives involve different trade-offs, I show that under many circumstances the optimal contest is one of the three basic contest structures widely studied in the literature: simultaneous, first-mover, or sequential contest.

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of $n$-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as "large $n$" equilibria.

In many real world situations, collective decisions are made using voting. Moreover, scenarios such as committee or board elections require voting rules that return multiple winners. In multi-winner approval voting (AV), an agent may vote for as many candidates as they wish. Winners are chosen by tallying up the votes and choosing the top-$k$ candidates receiving the most votes. An agent may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics to strategize, instead of incurring the additional effort required to compute the manipulation which most favors them.In this paper, we examine voting behavior in multi-winner approval voting scenarios with complete information. We show that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. Instead, voters tend to prioritize the candidates with the highest utilities. Using simulations, we demonstrate the effectiveness of these heuristics in situations where agents only have access to partial information.

When multiple firms are simultaneously running experiments on a platform, the treatment effects for one firm may depend on the experimentation policies of others. This paper presents a set of causal estimands that are relevant to such an environment. We also present an experimental design that is suitable for facilitating experimentation across multiple competitors in such an environment. Together, these can be used by a platform to run experiments "as a service," on behalf of its participating firms. We show that the causal estimands we develop are identified nonparametrically by the variation induced by the design, and present two scalable estimators that help measure them in typical high-dimensional situations. We implement the design on the advertising platform of JD.com, an eCommerce company, which is also a publisher of digital ads in China. We discuss how the design is engineered within the platform's auction-driven ad-allocation system, which is typical of modern, digital advertising marketplaces. Finally, we present results from a parallel experiment involving 16 advertisers and millions of JD.com users. These results showcase the importance of accommodating a role for interactions across experimenters and demonstrates the viability of the framework.

We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms resulting strategies are compared to classical stochastic control techniques on several payoffs using a variance criterion. One of the proposed algorithm is flexible enough to be used with several existing risk criteria. We furthermore propose a new moment-based risk criteria.

In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variables as (equivalent) martingale measures and prices consistent with the market model. Then, these dual representations are used to obtain the main results of this paper on time consistency for scalar risk measures in markets with frictions. It is well known from the superhedging risk measure in markets with transaction costs, as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied. We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process. We will prove the equivalence of this weaker notion of time consistency and a certain type of backward recursion with respect to the underlying risk measure with a fixed consistent pricing process. Several examples are given, with special emphasis on the superhedging risk measure.