In this paper, we provide (i) a rigorous general theory to elicit conditions on (tail-dependent) heavy-tailed cyber-risk distributions under which a risk management firm might find it (non)sustainable to provide aggregate cyber-risk coverage services for smart societies, and (ii)a real-data driven numerical study to validate claims made in theory assuming boundedly rational cyber-risk managers, alongside providing ideas to boost markets that aggregate dependent cyber-risks with heavy-tails.To the best of our knowledge, this is the only complete general theory till date on the feasibility of aggregate cyber-risk management.

We obtain error estimates for strong approximations of a diffusion with a diffusion matrix $\sigma$ and a drift b by the discrete time process defined recursively X_N((n+1)/N) = X_N(n/N)+N^{1/2}\sigma(X_N(n/N))\xi(n+1)+N^{-1}b(XN(n/N)); where \xi(n); n\geq 1 are i.i.d. random vectors, and apply this in order to approximate the fair price of a game option with a diffusion asset price evolution by values of Dynkin's games with payoffs based on the above discrete time processes. This provides an effective tool for computations of fair prices of game options with path dependent payoffs in a multi asset market with diffusion evolution.

In this paper we discuss the diffusion of serious games and present reasons for why Rogers traditional approach is limited in this context. We present an alternative overview through the characteristics of relative advantage, compatibility, complexity, trialability, and observability, that reflect on the adoption decision and contributes on the commercialization of serious games.

We propose a microscopic model to describe the dynamics of the fundamental events in the limit order book (LOB): order arrivals and cancellations. It is based on an operator algebra for individual orders and describes their effect on the LOB. The model inputs are arrival and cancellation rate distributions that emerge from individual behavior of traders, and we show how prices and liquidity arise from the LOB dynamics. In a simulation study we illustrate how the model works and highlight its sensitivity with respect to assumptions regarding the collective behavior of market participants. Empirically, we test the model on a LOB snapshot of XETRA, estimate several linearized model specifications, and conduct in- and out-of-sample forecasts.The in-sample results based on contemporaneous information suggest that our model describes returns very well, resulting in an adjusted $R^2$ of roughly 80%. In the more realistic setting where only past information enters the model, we observe an adjusted $R^2$ around 15%. The direction of the next return can be predicted (out-of-sample) with an accuracy above 75% for time horizons below 10 minutes. On average, we obtain an RMSPE that is 10 times lower than values documented in the literature.

In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized by an exponentially concave function on the unit interval. This choice can be motivated by the long term stability of the capital distribution observed in large equity markets, and allows us to circumvent the curse of dimensionality. The resulting optimization problem, which is convex, is flexible as various regularizations and constraints can be imposed on the generating function. We prove that the optimization problem is well-posed and provide a stability estimate in terms of a Wasserstein metric of the input measure. We then give a careful treatment of its discretization and the optimization algorithm. Finally, we present empirical examples using CRSP data from the US stock market.

It is a challenging task to identify the best possible models based on given empirical data of real stochastic time series. Though the financial markets provide us with a vast amount of empirical data, the best model selection is still a big challenge for researchers. The widely used long-range memory and self-similarity estimators give varying values of the parameters as these estimators themselves are developed for the specific models of time series. Here we investigate the order disbalance time series constructed from the limit order book data of the financial markets under fractional L\'{e}vy stable motion assumption. Our results suggest that previous findings of persistence in order flow are related to the power-law distribution of order sizes. Still, orders have stable estimates of anti-correlation for the 18 randomly selected stocks, when Absolute value and Higuchi's estimators are implemented. The burst duration analysis based on the first passage problem of time series and implemented in this research gives different estimates of the Hurst parameter more consistent with the uncorrelated increment cases.

The extent to which a matching engine can cloud the modelling of underlying order submission and management processes in a financial market remains an unanswered concern with regards to market models. Here we consider a 10-variate Hawkes process with simple rules to simulate common order types which are submitted to a matching engine. Hawkes processes can be used to model the time and order of events, and how these events relate to each other. However, they provide a freedom with regards to implementation mechanics relating to the prices and volumes of injected orders. This allows us to consider a reference Hawkes model and two additional models which have rules that change the behaviour of limit orders. The resulting trade and quote data from the simulations are then calibrated and compared with the original order generating process to determine the extent with which implementation rules can distort model parameters. Evidence from validation and hypothesis tests suggest that the true model specification can be significantly distorted by market mechanics, and that practical considerations not directly due to model specification can be important with regards to model identification within an inherently asynchronous trading environment.

Natural and anthropogenic disasters frequently affect both the supply and demand side of an economy. A striking recent example is the Covid-19 pandemic which has created severe disruptions to economic output in most countries. These direct shocks to supply and demand will propagate downstream and upstream through production networks. Given the exogenous shocks, we derive a lower bound on total shock propagation. We find that even in this best case scenario network effects substantially amplify the initial shocks. To obtain more realistic model predictions, we study the propagation of shocks bottom-up by imposing different rationing rules on industries if they are not able to satisfy incoming demand. Our results show that economic impacts depend strongly on the emergence of input bottlenecks, making the rationing assumption a key variable in predicting adverse economic impacts. We further establish that the magnitude of initial shocks and network density heavily influence model predictions.

The present work generalizes the analytical results of Petrikaite (2016) to a market where more than two firms interact. As a consequence, for a generic number of firms in the oligopoly model described by Janssen et al (2005), the relationship between the critical discount factor which sustains the monopoly collusive allocation and the share of perfectly informed buyers is non-monotonic, reaching a unique internal point of minimum. The first section locates the work within the proper economic framework. The second section hosts the analytical computations and the mathematical reasoning needed to derive the desired generalization, which mainly relies on the Leibniz rule for the differentiation under the integral sign and the Bounded Convergence Theorem.

Time inconsistency is prevalent in dynamic choice problems: a plan of actions to be taken in the future that is optimal for an agent today may not be optimal for the same agent in the future. If the agent is aware of this intra-personal conflict but unable to commit herself in the future to following the optimal plan today, the rational strategy for her today is to reconcile with her future selves, namely to correctly anticipate her actions in the future and then act today accordingly. Such a strategy is named intra-personal equilibrium and has been studied since as early as in the 1950s. A rigorous treatment in continuous-time settings, however, had not been available until a decade ago. Since then, the study on intra-personal equilibrium for time-inconsistent problems in continuous time has grown rapidly. In this chapter, we review the classical results and some recent development in this literature.