This model contains concept, equations, and graphical results for venture banking. A system of 27 equations describes the behavior of the venture-bank and underwriter system allowing phase-space type graphs that show where profits and losses occur. These results confirm and expand those obtained from the original spreadsheet based model. An example investment in a castle at a loss is provided to clarify concept. This model requires that all investments are in enterprises that create new utility value. The assessed utility value created is the new money out of which the venture bank and underwriter are paid. The model presented chooses parameters that ensure that the venture-bank experiences losses before the underwriter does. Parameters are: DIN Premium, 0.05; Clawback lien fraction, 0.77; Clawback bonds and equity futures discount, 1.5 x (USA 12 month LIBOR); Range of clawback bonds sold, 0 to 100%; Range of equity futures sold 0 to 70%.

We propose a new framework to value employee stock options (ESOs) that captures multiple exercises of different quantities over time. We also model the ESO holder's job termination risk and incorporate its impact on the payoffs of both vested and unvested ESOs. Numerical methods based on Fourier transform and finite differences are developed and implemented to solve the associated systems of PDEs. In addition, we introduce a new valuation method based on maturity randomization that yields analytic formulae for vested and unvested ESO costs. We examine the cost impact of job termination risk, exercise intensity, and various contractual features.

We introduce a simple model for equity index derivatives. The model generalizes well known L\`evy Normal Tempered Stable processes (e.g. NIG and VG) with time dependent parameters. It accurately fits Equity index implied volatility surfaces in the whole time range of quoted instruments, including small time horizon (few days) and long time horizon options (years). We prove that the model is an Additive process that is constructed using an Additive subordinator. This allows us to use classical L\`evy-type pricing techniques. We discuss the calibration issues in detail and we show that, in terms of mean squared error, calibration is on average two orders of magnitude better than both L\`evy processes and Self-similar alternatives. We show that even if the model loses the classical stationarity property of L\`evy processes, it presents interesting scaling properties for the calibrated parameters.

This paper extends the Singular Fourier--Pad\'e (SFP) method proposed by Chan (2018) to pricing/hedging early-exercise options--Bermudan, American and discrete-monitored barrier options--under a L\'evy process. The current SFP method is incorporated with the Filon--Clenshaw--Curtis (FCC) rules invented by Dom\'inguez et al. (2011), and we call the new method SFP--FCC. The main purpose of using the SFP--FCC method is to require a small number of terms to yield fast error convergence and to formulate option pricing and option Greek curves rather than individual prices/Greek values. We also numerically show that the SFP--FCC method can retain a global spectral convergence rate in option pricing and hedging when the risk-free probability density function is piecewise smooth. Moreover, the computational complexity of the method is $\mathcal{O}((L-1)(N+1)(\tilde{N} \log \tilde{N}) )$ with $N$ a (small) number of complex Fourier series terms, $\tilde{N}$ a number of Chebyshev series terms and $L$, the number of early-exercise/monitoring dates. Finally, we show that our method is more favourable than existing techniques in numerical experiments.

We study the optimal design of electricity contracts among a population of consumers with different needs. This question is tackled within the framework of Principal-Agent problems in presence of adverse selection. The particular features of electricity induce an unusual structure on the production cost, with no decreasing return to scale. We are nevertheless able to provide an explicit solution for the problem at hand. The optimal contracts are either linear or polynomial with respect to the consumption. Whenever the outside options offered by competitors are not uniform among the different type of consumers, we exhibit situations where the electricity provider should contract with consumers with either low or high appetite for electricity.

We examine the household-specific effects of the introduction of Time-of-Use (TOU) electricity pricing schemes. Using a causal forest (Athey and Imbens, 2016; Wager and Athey, 2018; Athey et al., 2019), we consider the association between past consumption and survey variables, and the effect of TOU pricing on household electricity demand. We describe the heterogeneity in household variables across quartiles of estimated demand response and utilise variable importance measures.

Household-specific estimates produced by a causal forest exhibit reasonable associations with covariates. For example, households that are younger, more educated, and that consume more electricity, are predicted to respond more to a new pricing scheme. In addition, variable importance measures suggest that some aspects of past consumption information may be more useful than survey information in producing these estimates.

Results of a convincing causal statistical inference related to socio-economic phenomena are treated as especially desired background for conducting various socio-economic programs or government interventions. Unfortunately, quite often real socio-economic issues do not fulfill restrictive assumptions of procedures of causal analysis proposed in the literature. This paper indicates certain empirical challenges and conceptual opportunities related to applications of procedures of data depth concept into a process of causal inference as to socio-economic phenomena. We show, how to apply a statistical functional depths in order to indicate factual and counterfactual distributions commonly used within procedures of causal inference. Thus a modification of Rubin causality concept is proposed, i.e., a centrality-oriented causality concept. The presented framework is especially useful in a context of conducting causal inference basing on official statistics, i.e., basing on already existing databases. Methodological considerations related to extremal depth, modified band depth, Fraiman-Muniz depth, and multivariate Wilcoxon sum rank statistic are illustrated by means of example related to a study of an impact of EU direct agricultural subsidies on a digital development in Poland in a period of 2012-2019.

This paper studies the forecasting ability of cryptocurrency time series. This study is about the four most capitalized cryptocurrencies: Bitcoin, Ethereum, Litecoin and Ripple. Different Bayesian models are compared, including models with constant and time-varying volatility, such as stochastic volatility and GARCH. Moreover, some crypto-predictors are included in the analysis, such as S\&P 500 and Nikkei 225. In this paper the results show that stochastic volatility is significantly outperforming the benchmark of VAR in both point and density forecasting. Using a different type of distribution, for the errors of the stochastic volatility the student-t distribution came out to be outperforming the standard normal approach.

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.

We propose a novel approach for loss reserving based on deep neural networks. The approach allows for joint modeling of paid losses and claims outstanding, and incorporation of heterogeneous inputs. We validate the models on loss reserving data across lines of business, and show that they improve on the predictive accuracy of existing stochastic methods. The models require minimal feature engineering and expert input, and can be automated to produce forecasts more frequently than manual workflows.

Forest management relies on the evaluation of silviculture practices. The increase in natural risk due to climate change makes it necessary to consider evaluation criteria that take natural risk into account. Risk integration in existing software requires advanced programming skills.We propose a user-friendly software to simulate even-aged and monospecific forest at the stand level, in order to evaluate and optimize forest management. The software gives the possibility to run management scenarii with or without considering the impact of natural risk. The control variables are the dates and rates of thinning and the cutting age.The risk model is based on a Poisson processus. The Faustmann approach, including tree damage risk, is used to evaluate future benefits, economic or ecosystem services. It relies on the calculation of expected values, for which a dedicated mathematical development has been done. The optimized criteria used to evaluate the various scenarii are the Faustmann value and the Averaged yield value.We illustrate the approach and the software on two case studies: economic optimization of a beech stand and carbon sequestration optimization of a pine stand.Software interface makes it easy for users to write their own (growth-tree damage-economic) models without advanced programming skills. The possibility to run management scenarii with/without considering the impact of natural risk may contribute improving silviculture guidelines and adapting them to climate change. We propose future lines of research and improvement.

In a discrete-time financial market, a generalized duality is established for model-free superhedging, given marginal distributions of the underlying asset. Contrary to prior studies, we do not require contingent claims to be upper semicontinuous, allowing for upper semi-analytic ones. The generalized duality stipulates an extended version of risk-neutral pricing. To compute the model-free superhedging price, one needs to find the supremum of expected values of a contingent claim, evaluated not directly under martingale (risk-neutral) measures, but along sequences of measures that converge, in an appropriate sense, to martingale ones. To derive the main result, we first establish a portfolio-constrained duality for upper semi-analytic contingent claims, relying on Choquet's capacitability theorem. As we gradually fade out the portfolio constraint, the generalized duality emerges through delicate probabilistic estimations.

Empirical research often cites observed choice responses to variation that shifts expected discounted future utilities, but not current utilities, as an intuitive source of information on time preferences. We study the identification of dynamic discrete choice models under such economically motivated exclusion restrictions on primitive utilities. We show that each exclusion restriction leads to an easily interpretable moment condition with the discount factor as the only unknown parameter. The identified set of discount factors that solves this condition is finite, but not necessarily a singleton. Consequently, in contrast to common intuition, an exclusion restriction does not in general give point identification. Finally, we show that exclusion restrictions have nontrivial empirical content: The implied moment conditions impose restrictions on choices that are absent from the unconstrained model.

Lead-lag relationships among assets represent a useful tool for analyzing high frequency financial data. However, research on these relationships predominantly focuses on correlation analyses for the dynamics of stock prices, spots and futures on market indexes, whereas foreign exchange data have been less explored. To provide a valuable insight on the nature of the lead-lag relationships in foreign exchange markets here we perform a detailed study for the one-minute log returns on exchange rates through three different approaches: i) lagged correlations, ii) lagged partial correlations and iii) Granger causality. In all studies, we find that even though for most pairs of exchange rates lagged effects are absent, there are many pairs which pass statistical significance tests. Out of the statistically significant relationships, we construct directed networks and investigate the influence of individual exchange rates through the PageRank algorithm. The algorithm, in general, ranks stock market indexes quoted in their respective currencies, as most influential. In contrast to the claims of the efficient market hypothesis, these findings suggest that all market information does not spread instantaneously.

We present a novel technique to solve the problem of managing optimally a pumped hydroelectric storage system. This technique relies on representing the system as a stochastic optimal control problem with state constraints, these latter corresponding to the finite volume of the reservoirs. Following the recent level-set approach presented in O. Bokanowski, A. Picarelli, H. Zidani, "State-constrained stochastic optimal control problems via reachability approach", SIAM J. Control and Optim. 54 (5) (2016), we transform the original constrained problem in an auxiliary unconstrained one in augmented state and control spaces, obtained by introducing an exact penalization of the original state constraints. The latter problem is fully treatable by classical dynamic programming arguments.

Investors usually resort to financial advisors to improve their investment process until the point of complete delegation on investment decisions. Surely, financial advice is potentially a correcting factor in investment decisions but, in the past, the media and regulators blamed biased advisors for manipulating the expectations of naive investors. In order to give an analytic formulation of the problem, we present an Agent-Based Model formed by individual investors and a financial advisor. We parametrize the games by considering a compromise for the financial advisor (between a sufficient reward by bank and to keep his/her reputation), and a compromise for the customers (between the desired return and the proposed return by advisor). Then we obtain the Nash equilibria and the best response functions of the resulting game. We also describe the parameter regions in which these points result acceptable equilibria and the greediness/naivety of the customers emerge naturally from the model. Finally, we focus on the efficiency of the best Nash equilibrium.

An investigation is presented of how a comprehensive choice of five most important measures of concordance (namely Spearman's rho, Kendall's tau, Spearman's footrule, Gini's gamma, and Blomqvist's beta) relate to non-exchangeability, i.e., asymmetry on copulas. Besides these results, the method proposed also seems to be new and may serve as a raw model for exploration of the relationship between a specific property of a copula and some of its measures of dependence structure, or perhaps the relationship between various measures of dependence structure themselves. In order to simplify the view on this method and provide a more conceptual interpretation a formulation is proposed borrowed from the imprecise probability setting which has been made possible for a standard probability method due to some recent discoveries.

We develop a general model for finding the optimal penal strategy based on the behavioral traits of the offenders. We focus on how the discount rate (level of time discounting) affects the criminal propensity on the individual level, and how the aggregation of these effects influences criminal activities on the population level. The effects are aggregated based on the distribution of discount rate among the population. We study this distribution empirically through a survey with 207 participants, and we show that it follows zero-inflated exponential distribution. We quantify the effectiveness of the penal strategy as its net utility for the population, and show how this quantity can be maximized. During the maximization procedure, we discover that the effectiveness of DWI deterrence depends critically on the amount of fine and prison condition.

We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic setting is time-inconsistency, that is, the usual "tower property" fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce a so-called distorted probability and construct a conditional expectation in such a way that it coincides with the original nonlinear expectation at time zero, but has a time-consistent dynamics in the sense that the tower property remains valid. Furthermore, we show that in the continuous time model this conditional expectation corresponds to a parabolic differential equation whose coefficient involves the law of the underlying diffusion. This work is the first step towards a new understanding of nonlinear expectations under probability distortion, and will potentially be a helpful tool for solving time-inconsistent stochastic optimization problems.

The binomial system is an electoral system unique in the world. It was used to elect the senators and deputies of Chile during 27 years, from the return of democracy in 1990 until 2017. In this paper we study the real voting power of the different political parties in the Senate of Chile during the whole binomial period. We not only consider the different legislative periods, but also any party changes between one period and the next. The real voting power is measured by considering power indices from cooperative game theory, which are based on the capability of the political parties to form winning coalitions. With this approach, we can do an analysis that goes beyond the simple count of parliamentary seats.